hydrology LECTURE.pdf

 DEFINITION OF HYDROLOGY Branch of science Deals with Origin or occurrence Circulation Distribution Of water of the earth and earth atmosphere Engineering Hydrology deals with ESTIMATION OF WATER RESOURCES STUDY OF PROCESSES SUCH AS PRECIPITATION, RUNOFF, EVAPOTRANSPIRATION AND THEIR...

 DEFINITION OF HYDROLOGY Branch of science Deals with Origin or occurrence Circulation Distribution Of water of the earth and earth atmosphere Engineering Hydrology deals with ESTIMATION OF WATER RESOURCES STUDY OF PROCESSES SUCH AS PRECIPITATION, RUNOFF, EVAPOTRANSPIRATION AND THEIR INTERACTION STUDY OF FLOODS AND DROUGHTS Importance of Engineering Hydrology üDeciding on the need to manage the water resources of an area üDetermination of the sources of water and the available quantity/quality üChecking the completeness and consistency of the data üEstimation of average rainfall over an area üEstimation of flow in a stream due to rainfall in the catchment area üWhat should be the storage capacity of the reservoir üWhat is the safe limit for withdrawing water from the groundwater üWhat kind of the extreme hydrological events could be expected in an area and what is the probability of such occurences A watershed or catchment basin is a contiguous area that drains to a common outlet. It is the area around a stream that actually sends water into the stream. The drainage divide is the locus of points that separates adjacent watersheds. Watershed delineated on a topographic map Watershed water balance P E+T P - R - G - E - T = DS Q S G The Hydrologic Cycle Atmospheric Moisture Moisture over land Precipitation on land 61 P Evaporation from land Precipitation on ocean Snow melt Runoff Evap Surface runoff Precipitation ET Evap Evaporation from ocean Infiltration Streams Groundwater Wa ter t Recharge able Runoff Surface discharge Groundwater flow 1 Groundwater Lake Impervious strata GW discharge Reservoir 1. Surface reservoir 2. Subsurface reservoir 3. Atmospheric reservoir EACH PATH OF HYDROLOGIC CYCLE INVOLVES FOLLOWING ASPECTS — TRANSPORTATION OF WATER (precipitation, evaporation, transpiration, runoff, infiltration) — TEMPORARY STORAGE (depression storage, lakes, reservoirs, ponds, soil moisture storage, groundwater storage)) — CHANGE OF STATE PROCESS OF RAINFALL HAS CHANGE OF STATE AND TRANSPORTATION ASPECTS GROUNDWATER PATH HAS STORAGE & TRANSPORTATION ASPECTS Interception (part of Evap., E) — LOSS: Interception loss is that part of the precipitation that falls on plants and doesn't reach the ground. It evaporates (or sublimates) from leaves, near-ground plants and leaf litter or, to a lesser extent, is absorbed by plants  Interflow and Base Flow Interflow may reach the surface prior to the stream channel Baseflow is saturated zone water that flows into the channel. The stream runs even when it hasn’t been raining. Storm Water Component Sequence  Water Balance Atmospheric Water Soil Water Surface Water Groundwater Change of Inflow – Outflow = Storage dS I -Q = dt  WATER BUDGET EQUATION Inputs Outputs (Losses) (Gains) P = precipitation E = evaporation I = inflow T = transpiration (these are commonly combined to make “ET” = E + T) R = surface runoff at outlet G = groundwater flow  WORLD WATER QUANTITIES LIQUID STATE (30.3%) FRESH WATER (2.5%) ALL KINDS OF FROGEN STATE WATER (69.7%) SALINE WATER (97.5%) 3 ALL KINDS OF WATER : 1386 M KM 3 SALINE WATER: 1351 M KM (97.5 %) 3 FRESH WATER: 35 M KM (2.5%) 3 3 10.6 M KM IS LIQUID STATE AND 24.4 M KM IS FROGEN STATE  WORLD WATER BALANCE ITEMS OCEAN LAND 3 Precipitation (M KM ) 0.458 0.119 3 Evaporation (M KM ) 0.505 0.072 3 3 Remarks 0.047 M KM 0.047 M KM more more evaporation precipitation REMARKS: 1. Precipitation is less than evaporation in ocean 2. Precipitation is more than evaporation in land 3. It is found that 9% more water evaporates in ocean in comparison to precipitation 3 4. 0.047 M KM is the runoff from land to ocean  WORLD WATER BALANCE RESIDENCE TIME: The average duration of a particle of water to pass through a phase of the hydrologic cycle is known as residence time of that phase. Residence time =Volume of water in the phase/average flow rate in that phase It varies from phase to phase  General points on hydrologic cycle 1. The cycle is not spatially uniform. Some areas may experience intense rainfall while other nearby areas may be completely dry. 2. The cycle is not temporarily steady. The same areas may get intense rain at a time and completely dry at other times 3. Movement of water through various phases of the cycle could be obtained through an average residence time. Ex: It is estimated that atmospheric reservoir has a storage volume of about 13000 km3 and it transfers water at a rate about 500000 km3/year. On an average water drop will stay in atmosphere for 9-10 days. River water has residence time of 2-6 months, oceans 3000 years, shallow groundwater about 100 years and deep groundwater about 10000 years. 4. Changing climate may have significant effect on the hydrologic cycle.  QUIZ QUESTION A catchment area 120 km2 has three distinct zones. The annual runoff from the catchment is____. zone Area km2 Annual runoff (cm) A 61 52 B 39 42 C 20 32 a. 126 cm b. 42 cm c. 45.4 cm d. 47.3 cm  PRECIPITATION Precipitation is any type of water that forms in the Earth's atmosphere and then drops onto the surface of the Earth.  Sleet Rain Hail Snow  PRECIPITATION To form precipitation — Atmosphere must have the moisture — There must be sufficient nuclei present to aid condensation (Nuclei are usually salt particles or products of combustion). — Weather condition must be good for condensation of water vapour to take place — The product of condensation must reach to the earth Water vapor, droplets of water suspended in the air, Water vapor in the atmosphere is builds up in the Earth's visible as clouds and fog. atmosphere. Water vapor collects with other materials, such as dust, in clouds. Clouds Precipitation eventually get condenses, or too full of water forms, around vapor, and the these tiny pieces of precipitation material, called turns into a cloud liquid (rain) or a condensation solid (snow). nuclei (CCN). Precipitation Starts With Different Air Masses Being Pushed Around by Global Winds High pressured air mass Warm, Dry air Wet, humid mass air mass Cold air mass Low pressured air mass Obviously, these moving air masses will eventually bump into one another. When 2 or more different air masses meet, the place where they bump is called… Front Warm air mass Cold air mass A storm, usually with precipitation, occurs at this front.  The type of precipitation that falls from the clouds to the surface of the Earth depends on ONE main thing… TEMPERATURE The temperature of the clouds vs. the temperature of the surface air.  RAIN Rain occurs when precipitation falls from the clouds as liquid water. During a rain storm, the temperature is warm in the clouds and… WARM Clouds warm at ground level so... Warm surface precipitation is in melted, liquid form. Light rain Upto 2.5 mm/hour Moderate rain 2.5-7.5 mm/hour Heavy rain > 7.5 mm/hour  SNOW SNOW OCCURS WHEN PRECIPITATION FALLS FROM THE CLOUDS AS COLD, FLAKY SOLIDS. DURING A SNOW STORM, THE TEMPERATURE IN THE CLOUDS FREEZING COLD CLOUDS IS VERY COLD WHICH FREEZES THE RAIN INTO ICE CRYSTALS AND… IT IS ALSO COLD AT GROUND LEVEL SO… FREEZING COLD PRECIPITATION IS SURFACE FROZEN SOLID IN THE CLOUDS AND STAYS FROZEN BY THE COLD SURFACE.  Sleet occurs when precipitation falls from Sleet the clouds to the ground as half water/half ice. During a sleet storm, the temperature of the clouds is warm, so Warm Clouds the precipitation begins to fall as… liquid rain. But, the air around the surface is very cold, so it begins to freeze the Freezing Cold surface liquid into a slushy solid. This slushy solid, which is half frozen, falls to the ground as sleet. Sleet storms are sometimes called ice storms. Because the surface temperature is very cold during a sleet storm and everything usually gets covered in ice. Hail is precipitation that falls from the clouds to the surface as balls of ice (Sizes vary from 0.5 to 5 cm in dia). HAIL Freezing Cold Clouds and grows, Precipitatio But it gets and grows n in the pushed back and grows, form of ice up by the until… begins to strong wind fall from the back into the A hail storm begins clouds. clouds where with warm surface temperatures. Very it joins with more ice and The hail stones become so strong, warm wind grows… heavy, the wind can’t hold currents push upward them up in the clouds and toward the cold clouds. they fall to the warm If the upward wind currents are normal, hail stones will usually be as big as marbles. But if the wind currents are very strong (over 100 miles per hour), the hail stones can stay These large hailstones cause lots of up in the cold clouds for a long damage to cars, homes, crops and time and grow very large. people. Drizzle A fine sprinkle of numerous water droplets of size less than 0.5 mm and intensity less than 1mm/hr is known as drizzle. Glaze When rain or drizzle comes in contact with cold ground at around 00C, the water drops freeze to form an ice coating called glaze. A front is the interface between two distinct air masses. When a warm air mass and cold air mass meet, the warmer air mass is lifted over the colder one with the formation of a front. The ascending warmer air cools adiabatically with consequent formation of clouds and precipitation.  CONVECTIVE PRECIPITATION Areal extent of such rain is usually limited to diameter of about 10 km. OROGRAPHIC PRECIPITATION TROPICAL CYCLONE  A cyclone is a large low pressure region with circular wind motion Two types of cyclones: Tropical cyclone and extra tropical cyclone Tropical cyclone is a wind system with an intensely strong depression with MSL pressure below 915 mbars Normal areal extent of a cyclone is 100-200 km in diameter Winds are anticlockwise in northern hemisphere and clockwise in southern hemisphere Centre of the storm is known as eye of 10-50 km in diameter will be relatively quiet. Right outside eye, very strong wind 200 kmph. Wind speed gradually decreases towards the outer edge Pressure increases outwards Derive energy from latent heat of condensation of ocean water vapour and increase in size as they move on oceans When they move on land, the source of energy cutoff and dissipates very fast. Intensity of storm decreases rapidly  Extra tropical cyclone Formed outside the tropical zone Associated with frontal system, possess strong counter clockwise wind circulation in northern hemisphere Magnitude of precipitation and wind velocity is relatively lower than tropical cyclone Duration and areal extent is larger Anticyclone These are the regions of high pressure Weather is usually calm at centre Clockwise wind circulation in northern hemisphere Measurement of Rainfall — Rainfall and other forms of precipitation are measured in terms of depth, the values being expressed in millimeters, centimeters, inches — One millimeter of precipitation represents the quantity of water needed to cover the land with a 1mm layer of water — Hence expressed in terms of the vertical depth to which water would stand on a level surface area if all the water from it were collected on this surface — Instrument used to collect and measure the precipitation is called raingauge. Placement of Rain Gauge — The ground must be level, open so that instrument must represent a horizontal catch surface — Must be set as near the ground as possible to reduce wind effects — Must be set sufficiently high to prevent splashing, flooding etc — The instrument must be surrounded by an open fenced area Type of rain gauges — Non recording — Recording type — Have rainfall recording Used for measurement of mechanism amount of rainfall — It allows continuous by collecting over a period measurement of the of time rainfall. — Two types: — Type: — Symon Rain gauge — Tipping Bucket Type — Indian Standard (IS:5225- — Weighing Bucket Type 1969) — Natural Syphon Type — Telemetering Raingauges — Radar measurement SYMON’S RAINGAUGE Collector Size: 100 or 200 sq.cm Capacity of bottle: 2,4 or 10 litres Capacity of raingauge: 100, 200, 400, 500, 1000 mm 200 sq cm collector size, 4 liter bottle size is commonly used Tipping and Weighing type rain gauge Float type self recording raingauge  RAINGAUGE NETWORK WMO RECOMMENDATION vIn flat regions of temperate, mediterranean and tropical zone Ideal: 1 station for 600-900 km2 Acceptable: 1 station for 900-3000 km2 vIn mountainous regions of temperate, mediterranean and tropical zone Ideal: 1 station for 100-250 km2 Acceptable: 1 station for 250-1000 km2 vIn arid and polar zones Ideal: 1 station for 1500-10000 km2 vTen percent of raingauge stations should be equipped with self recording gauge to know the intensity of rainfall ADEQUACY OF RAINGAUGE STATIONS 2 æ CV ö N =ç ÷ è e ø 100 ´ s M -1 N= Optimal number of stations CV = P ε = Allowable degree of error in the éM 2 ù ê å (Pi - P ) ú estimate of the mean rainfall Cv = Coefficient of variation of the s M -1 = ê 1 ú ê M -1 ú rainfall values at the existing M êë úû stations in the catchment 1 æM ö σM-1 = Standard deviation P= ç å Pi ÷ Mè 1 ø 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 rainfall, calculate the optimum number of stations in the catchment. Station A B C D E F Rainfall (cm) 82.6 102.9 180.3 110.3 98.8 136.7 Representation of Point Rainfall — Mass Curve — Hyetograph — Obtained from — Plot of rainfall intensity recording type rain vs time gauge — Shown in form of bar — Is a plot of accumulated charts precipitation vs time — Area under curve is total — Gives information on depth of ppt magnitude, duration and intensity of rainfall ESTIMATION OF MISSING DATA If the normal annual precipitations at various stations are within about 10% of normal annual precipitation at station X, then simple arithmatic average is used to estimate Px. If the normal annual precipitations at various stations are beyond 10% of normal annual precipitation at station X, then normal ratio method is used to estimate Px. 1 PX = [ P1 + P2 + P3 + - - - - - - - PM ] M N é P1 P2 P3 PM ù PX = X ê + + +------- ú M N ë 1 N 2 N 3 N M û  TEST FOR CONSISTENCY Common causes of inconsistency ØShifting of raingauge station to a new location ØThe neighbourhood of the station undergoing a marked change ØChange in the ecosystem due to calamities such as forest fires, land slides etc. ØOccurrence of observational error from a certain date PROCEDURE: ØA group of 5-10 base stations in the neighbourhood of the problem station X is selected ØThe data of the annual rainfall of the station X and also the average rainfall of the group of base stations covering a long period is arranged in reverse chronological order. ØThe accumulated precipitation of station X and the accumulated values of the average of the group of the base station are calculated starting from the latest record. ØValues of accumulated precipitation of station are plotted against accumulated values of the average of the group of the base station  MC PCX = PX MA PCX = Corrected precipitation at any time period at station X PX = Original recorded precipitation at same time period at station X Year Annual Average Annual Year Annual Average Annual rainfall of a rainfall of the rainfall of a rainfall of the station group station group 1950 676 780 1965 1244 1400 1951 578 660 1966 999 1140 1952 95 110 1967 573 650 1953 462 520 1968 596 646 1954 472 540 1969 375 350 1955 699 800 1970 635 590 1956 479 540 1971 497 490 1957 431 490 1972 386 400 1958 493 560 1973 438 390 1959 503 575 1974 568 570 1960 415 480 1975 356 377 1961 531 600 1976 685 653 1962 504 580 1977 825 787 1963 828 950 1978 426 410 1964 679 770 1979 612 588 MEAN PRECIPITATION OVER AN AREA 1. ARITHMATIC MEAN METHOD 2. THIESSEN-MEAN METHOD 3. ISOHYETAL METHOD 1. ARITHMATIC MEAN METHOD When the rainfall measured at various stations in a catchment show little variation, the average precipitation over the catchment area is taken as arithmatic mean of the of the station values 1 P= [ P1 + P2 + P3 + - - - - - - - PM ] M  Method of Thiessen polygons The method of Thiessen polygons consists of attributing to each station an influence zone in which it is considered that the rainfall is equivalent to that of the station. The influence zones are represented by convex polygons. These polygons are obtained using the mediators of the segments which link each station to the closest neighbouring stations  The basin area is plotted to some scale and on the same map the locations of the raingauge stations both within the area and also outside the area but nearby are indicated. Straight lines are drawn joining adjacent raingauge locations to form triangles. Whenever it is required to divide a quadrilateral into two triangles, the shorter diagonal is preferred. Perpendicular bisectors are drawn to each side of triangles. These bisectors define a set of polygons one for each gauge. The polygon areas around each raingauge stations within the basin boundary are measured. Thiessen polygons ……….  Thiessen polygons ………. P7 P6 A7 A6 P2 A2 A1 A8 A5 P1 P8 P5 A3 A4 P3 P4  Thiessen polygons ………. P1 A1 + P2 A2 +..... + Pm Am P = ( A1 + A2 +..... + Am ) Generally for M station M åPA i i M Ai P = i =1 Atotal = å i =1 Pi A Ai The ratio is called the weightage factor of station i A THIESSEN POLYGON METHOD Isohyetal Method An isohyet is a line joining points of equal rainfall magnitude. 10.0 8 D 6 C a5 12 9.2 12 a4 7.0 a3 4 B 7.2 A a2 E 10.0 9.1 4.0 a1 F 8 6 4 Isohyetal Method P1, P2, P3, …. , Pn – the values of the isohytes a1, a2, a3, …., a4 – are the inter isohytes area respectively A – the total catchment area P - the mean precipitation over the catchment æ P1 + P2 ö æ P2 + P3 ö æ Pn-1 + Pn ö a1 ç ÷ + a2 ç ÷ +... + a n-1 ç ÷ è 2 ø è 2 ø è 2 ø P = A NOTE The isohyet method is superior to the other two methods especially when the stations are large in number.  DAD CURVES Information on the maximum amount of rainfall of various durations occurring over various sizes of areas is required inorder to estimate severe flood. DAD analysis forms an important aspect of hydro meteoroloical study. For a rainfall of a given duration, the average depth decreases with the area in an exponential manner ( P = P0 exp - KAn ) P0 is Highest amount of rainfall in cm at the storm centre and K and n are constants for a given region P is average depth in cm over an area The exact determination of average depth is not possible as the storm centre never coincides with a raingauge station. Hence in the analysis of large area storms the highest station rainfall is taken as the average depth over an area of 25 km2. 1. Severemost rainstorms that have occurred in the region are considered 2. Isohyetl maps and mass curves are compiled 3. Depth-area curve of a given duration of the storm is prepared 4. From mass curve of rainfall, various durations and the maximum depth of rainfall in these durations are noted 5. The maximum Depth-Area curve for a duration D is prepared by assuming the area distribution of rainfall for smaller duration to be similar to the total storm. 6. The above procedure is repeated for different storms and envelope curve of maximum depth-area for duration D is obtained. A similar procedure for various values of D results of a fam8ily of envelope curve of maximum depth vs area with duration as third parameter. TYPICAL DAD CURVES FREQUENCY OF POINT RAINFALL Probability of occurrence of a particular extreme rainfall will be important in design of hydraulic structures. Such information is obtained by the frequency analysis. Time series: The rainfall at a place is a random hydrologic process and a sequence of rainfall data at a place when arranged in chronological order constitute a time series. Return period: The probability of occurrence of an event of a random variable whose magnitude is equal to or in excess of a specified magnitude X is denoted by P. The recurrence interval or Return period T = 1/P This represents the average interval between the occurrence of a rainfall of magnitude equal to or greater than X.  FREQUENCY OF POINT RAINFALL If the probability of an event occurring is P, The probability of the event not occurring in a given year is q = 1-P The probability of occurrence of an event r times in n successive years n! Pr ,n = n C r Pr q n - r = P r q n-r (n - r )!r! The probability of the event not occurring at all in n successive years is P0,n = q n = (1 - P ) n The probability of the event not occurring atleast once in n successive years is P1 = 1 - q n = 1 - (1 - P ) n PLOTTING POSITION FORMULAE The purpose of frequency analysis of an annual series is to obtain a relation between the magnitude of an event and its probability of exceedence. The probability analysis may be made by empirical or analytical methods The exceedence probability of the event obtained by the use of an empirical formula is called plotting position. Weibull formula is the most popular plotting position formula. After calculating P and T for all event in series, the variation of the rainfall magnitude is plotted against the corresponding T on a semi-log or log-log paper. By suitable extrapolation of the plot, the rainfall magnitude of specific return period can be estimated. This give good results for small extrapolation and the error increases with amount of extrapolation 75% dependable annual rainfall at a station means the value of annual rainfall at the station that can be expected to be equaled to or exceeded 75% times. 75% dependable annual rainfall means the value of rainfall in the annual rainfall time series that has P =0.75 or T = 1.333 years PLOTTING POSITION FORMULAE The annual rainfalls at a place for a period of 19 years from 1970 to 1988 are given below 520, 615, 420, 270, 305, 380, 705, 600, 350, 550, 560, 400, 520, 435, 395, 290, 430, 1020,900. Construct the frequency curve and find 75% and 50% dependable rainfall. What is the probability that a rainfall of 800 mm or more occurs in any year.  MAXIMUM INTENSITY-DURATION-FREQUENCY RELATIONSHIP Maximum Intensity duration relationship 1. Select a convenient time step Dt such that duration of the storm D = N. Dt 2. For each duration (say tj = j. Dt) the mass curve of rainfall is considered to be divided into consecutive segments of duration tj. For each segment the incremental rainfall dj in duration tj is noted and intensity Ij = dj / tj obtained. 3. Maximum value of intensity for the chosen tj is noted. 4. The procedure is repeated for all values of j = 1 to N to obtain datasets of intensity as a function of duration. Plot the maximum intensity vs duration. Maximum depth-duration relationship 1. The product of maximum intensity with duration will be maximum depth of precipitation in the duration t.  MAXIMUM INTENSITY-DURATION-FREQUENCY RELATIONSHIP Maximum Intensity duration-frequency relationship 1. M number of significant and heavy storms in a particular Year Y are selected for analysis. Each of these storms are analysed for maximum intensity duration relationship 2. This gives the set of maximum intensity as a function of duration for the year Y 3. This procedure is repeated for all N years of record to obtain the maximum intensity Im (Dj )k for all j= 1 to M and k = 1 to N. 4. Each record of Im (Dj )k for k= 1to N constitutes a time series which can be analysed to obtain frequencies of occurrence of various Im (Dj ) values. Thus there will be M time series generated. 5. The results are plotted as maximum intensity vs return period with the duration as third parameter.  MAXIMUM INTENSITY-DURATION-FREQUENCY RELATIONSHIP KT x i= ( D + a )n i = maximum intensity cm/hr T= return period years D = duration hours K,x,a,n are coefficients for the area represented by station Prepare the maximum depth duration curve, maximum intensity duration curve for the 90 minute storm given below Time 0 10 20 30 40 50 60 70 80 90 (min) Cumul 0 8 15 25 30 46 55 60 64 67 ative rainfall (mm) The mass curve of rainfall in a storm of total duration 270 minutes is given below. Plot the maximum intensity-duration curve for this storm Time 0 30 60 90 120 150 180 210 240 270 (min) Cumul 0 6 18 21 36 43 49 52 53 54 ative rainfall (mm)  PROBABLE MAXIMUM PRECIPITATION (PMP) The Probable maximum precipitation is defined as the greatest or extreme rainfall for a given duration that is physically possible over a station or basin From operational point of view PMP can be defined as that rainfall over a basin which would produce a flood flow with virtually no risk of being exceeded PMP = P + Ks P (bar) = Mean of annual maximum rainfall series sIs standard deviation of the series K is a frequency factor which depends upon statistical distribution of the series, number of years of record and the return period