Effects of storage

• No storage no change in storage I = Q

• Large storage big differences between inflow and outflow

Estimate streamflow

• Given Inflow (I) and Storage S = f(Q)

• Calculate change in storage:

Δ S = S2 – S1

= [(I1+I2)/2 – (Q1 + Q2)/2] ΔT

S2 + Q2 ΔT/2 = S1 + [(I1 + I2) – Q1] ΔT/2

Right Hand Side (RHS): all the known terms

Use relationship between S and Q

Example

Time

(hours)

Excess

Rainfall

(mm)

0 0

1 10

2 20

3 5

4 0

QS 14102

constant baseflow of: 10 m3s-1

catchment area: 24 km2

Estimate hydrograph

Time

(hours)

Excess

Rainfall

hyetograph

(mm)

Excess

rainfall in

flow units

(m3s

-1)

Baseflow

(m3s

-1)

Storage

(m3) RHS

Direct

Runoff

(m3s

-1)

Runoff

(m3s

-1)

0 0 0.0 10 0 0.0 10.0

1 10 66.7 10 106417 120000 7.5 17.5

2 20 133.3 10 401576 452834 28.5 38.5

3 5 33.3 10 576706 650318 40.9 50.9

4 0 0.0 10 499356 563095 35.4 45.4

5 10 386309 435618 27.4 37.4

6 10 298854 337000 21.2 31.2

7 10 231197 260707 16.4 26.4

8 10 178857 201687 12.7 22.7

9 10 138366 156028 9.8 19.8

10 10 107042 120705 7.6 17.6

11 10 82809 93379 5.9 15.9

12 10 64062 72239 4.5 14.5

13 10 49559 55885 3.5 13.5

14 10 38340 43234 2.7 12.7

15 10 29660 33446 2.1 12.1

16 10 22946 25874 1.6 11.6

17 10 17751 20017 1.3 11.3

18 10 13732 15485 1.0 11.0

19 10 10624 11980 0.8 10.8

20 10 8219 9268 0.6 10.6

21 10 6358 7170 0.5 10.5

22 10 4919 5546 0.3 10.3

23 10 3805 4291 0.3 10.3

24 10 2944 3319 0.2 10.2

25 10 2277 2568 0.2 10.2

26 10 1762 1987 0.1 10.1

27 10 1363 1537 0.1 10.1

28 10 1054 1189 0.1 10.1

29 10 816 920 0.1 10.1

30 10 631 712 0.0 10.0

Example:

What is the probability of a 1 in 10 year ARI flood occurring at-least once in a 10 year period? Hence, probability of at-least one, ARI 10 year flood in 10 years = 1 – (1-p)^10

= 1 – (1-0.1)10 = 0.65

What is the probability that there will be exactly 1 flood of ARI 10 years in a 10 year period?

Flood Frequency Analysis

The procedures are primarily for use in estimating the peak flows, although they may be applied for estimating the flood volumes too.

Analysis may be done on Annual flood series or partial flood series. Annual flood series refer to the series of maximum flows in any given year. Hence, to record this series, one has to record the maximum flow at any given point in time in a calendar year.

- Partial flood series refers to the series of peak discharges above a certain base value. So it does not matter whether more than one values are collected from a single year, and none from another year.

We shall be using annual series in the tutorial and assignment questions in this course.

- The annual or partial flow series much have independent values in it. This means, that if the maximum flow in 1987 occurred on December 31st and in 1988 on January 1st, we would not use the

January 1st, 1988 flow as part of our annual flood series. This is since both are likely to the result of the same storm events and may not be statistically independent of each other.

Flood frequency analysis involves the following main steps:

1. Recording the flood series - If it is an annual flood series we are working with, only the independent maximum annual flow values form part of the series.

2. plotting the Annual Exceedance Probabilities (AEP) vs flood discharge - The AEP's are estimated based on the rank of the flood values. These AEP's are referred to as Plotting Positions of the flood series.

3. Fitting a probability distribution to the flood series

4. Plotting the design discharges corresponding to various AEP's estimated based on the fitted probability distribution on sample graph used in step 2.

5. Plotting the confidence limits associated with the probability distribution to verify whether the fit is an adequate representation of the actual flood series.

6. Reading off the value of the design discharge

Non-stationary: PDF changes overtime due to – urbanization, deforestation and climate change

Estimate a design flood:

No rainfall data: extrapolate storm using data from nearby station or area with similar attributes but adjust some variables.

Lots of flow data: Form a sample of annual max flow, fit probability distribution then estimate Qy.

Lots of rainfall data: Simulate flow using model and do flood frequency analysis, estimate design and use this to derive Qy

Q. The annual maximum flows collected to perform a flood frequency analysis are not independent

• Effectively number of data points will be fewer

• Will impact on the uncertainty of the estimates – plus will end up biasing the parameter estimates towards the dependent data points

The Average Recurrence Interval (ARI) is the average or expected value of the period between exceedences of a given discharge. Hence a 100 year ARI flood refers to the flood which can be expected to occur on the average once in 100 years. The Annual Exceedence Probability (AEP) refers to the probability of exceedence of a given flood level. A flood with an AEP of 0.01 means the flood can be exceeded with a 1% probability, or, the flood is a 1 in 100 year flood (the ARI being equal to 100 in this case). The AEP is usually expressed as 1 in Y, eg. 1 in 100. *It should be noted that the ARI or AEP indicate the probability of occurrence of a flood on a yearly basis. Hence, an ARI of 10 years implies that the probability of a flood occurring in a given year is 1/10, or, on average, one can expect the flood equaling or exceeding the design magnitude to occur once in 10 years. It does not mean that there is a certainty that a 1 in 10 year flood will occur once in 10 years. Pan Evaporation is the direct method to measure the evaporation. Whereas Penman-Monteith equation, indirect method, requires measurement of variables. The main assumption that makes them very different to each other is that the water and cropped surface produce significant difference water loss from an open water surface and the crop, also assuming in both have unlimited supply of water (Fao.org, 2014). Therefore, when translating Ep to ET0 there must be a correction factor, kp. This correction factor represent the differences between the two methods. The correction factor range of a “Class A” pan is between 0.60 and 0.80(The Constructor, 2010). Althrough, the Penman-Monteith equation is quite reliable since it takes many parameters into account in its equation. It’s often used only for estimating evatranspiration of farmlands, but this isn’t completely perfect for the use since the rs value, net resistance to diffusion through the surfaces of the leaves and soil, is a uniform depending on the type of vegetation of the land. The estimation could get even worse if the land contains a large area of non-vegetation (Ward and Robinson, 1999). Therefore in this case I wouldn’t say that the values of 7.6mm and 4.8401 mm are reliable since Sydney has a lot of infrastructures which is contrary to the main assumption of the two methods. Also an inadequate amount of the data which given to be used in calculating ET0, since the ET0 is very sensitive with changes of data Thornthwaite’s method is based on an empirical correlation between mean air temperature and transpiration rate. It’s relatively simple to compute compare to the Penman-Monteith’s method. Given the monthly mean temperatures from the measurements at a climatological station, an estimate of the potential evaporation for each month of the year can be calculated. It has been one of the most misused empirical equations in arid and semi-arid, which Australia is, irrigated areas where the requirement has not been maintained” - A bridge is designed t0 withstand a 200 years ARI flood. What is the prob. That it will suffer excessive damage in first 100 years ○ Assume that a single flood larger than the design flood is sufficient to incur excessive damage ○ AEP=1/200 = 0.0005 - P(e)=(100C0)*(0.005)^(0)*(1-0.005)^100 ; probability that 0 flood of 200ARI will occur in 100 years - P(e)=0.605 Probability that >= 1 flood will occur in 100 years : 1-P(e)= 1 - 0.605 = 0.395 = 39.5%

Lecture 1

The hydrological cycle - “The distribution and spatial and

temporal variation of water in the terrestrial, oceanic and

atmospheric compartments of the global system.”

Conceptual model that describes the storage and movement of water in the Earth system essentially between reservoirs

- Water is renewed in rivers once every 16 days. Water in the atmosphere is completely replaced every 8 days.

The SUN - The peak of the Sun's energy output is in the visible light range. Visible light has a wavelength between 0.4-0.71 μm, σ = 5.67 x 10-8 W.m-2K-4, λmT = 2877 μm K

Energy leaving the sun,S0 = 65 x 106 W.m-2, Rsun = 700 x 106 m Rearth = 6.4 x 106 m, Distance (earth to the sun) DSE = 150 x 109 m S=1368w/m2(circle) -> S=342w/m2(sphere) SA=4piR2

Energy Cycle - Earth’s radiation balance, Vertical energy balance, Latitudinal energy balance, Seasonal and diurnal cycles - Earth’s axis is not perpendicular to the plane of orbit around the Sun, but is tilted ~23.5° from it, The Greenhouse Effect, Ocean Circulation

**Energy Transport – Sunlight warms the surface: convection moves heat/vapor from tropics (warm air rises, cold air sinks!) Circulation breaks up into 3 cells, Hardly,Ferrell in each hemisphere. When vapor condenses as rain it release latent heat, warmning the air and driving circulation.

Q2. Name and explain any mechanism that could produce i) cyclical climate fluctuations; ii) a linear trend; or iii) a sudden increase or decrease in temperature?

1. diurnal and seasonal changes in solar output are cyclical. It is possible that the cyclical nature of sunspots could influence the climate. The orbital variations proposed by Milankovitch are also cyclical.

2. an increase in solar output or increases in greenhouse gases could cause a linear temperature increase.

3. a sudden temperature change could result from changes in volcanic activity – or interruption of the thermohaline circulation (by sudden influx of melt-water). It is now thought that ocean circulation can change on the order of decades. What would be the impact of parts of an catchment being urbanized (increase imperviousness) on:

- Rainfall (no direct effect, but will affect the depth and volume of rainfall)

- Duration: Peak duration is quicker

–Flood hydrograph: Shorter Quicker peak higher peak

Lecture 2

Climate is what you expect – weather is what you get.

Natural climate variability

External influences: diurnal, seasonal, millennial cycles of insolation – Sunspot, Milankovic{Eccentricity cycle (due to the gravitational fields of Jupiter and Saturn.), oblique cycle, precession equinox}, Naturally occurring random fluctuations (volcanic eruptions {eject huge quantities of sulfates and aerosols into the stratosphere }, meteor{Ozone destroyed, High surface temp}) Longer term weather fluctuations (El-Niño, ENSO, PDO)

Non-linear feedback mechanisms, Anthropogenic changes(GHG, ozone depletion) Summary - Milankovitch cycles – 25000 – 100000 years/ Ocean circulation – thousands of years/ Sunspots – decadal to hundreds of years/ Teleconnections – annual to decadal/ Volcanos?

Reconstruct climate using:

-Tree rings(carbon 14 dating, isotope decays half-life)

-Pollen records, Fuana and flora(sea cores),isotope-coral,icecore

Eamian interglacial is the closest past analogy of the present interglacial.

Climate Change – Human activities induce by: land use patterns, urban climate, aerosols other pollutant, deforestation

GHG – Atmosphere consists of approximately 78% N and 21% O2 – mainly transparent to SW and LW radiation // H2O and CO2 are largely transparent to SW↓, but strongly absorb the LW // Biggest absorber is water vapour, which is not well mixed and may vary from 0.01% - 3%.

Atmosphere

- 1 Atm = 101.325 kPa = 1013.25 mb

Vapor pressure (ed): the pressure of a vapor in equilibrium with its liquid and solid phases. Relates to tendency of molecules to escape from a liquid or a solid (evaporate)

Saturated vapor pressure (es) is the vapor pressure when molecules evaporating = molecules condensing.

Dew point temperature: For a known the amount of water vapour in the atmosphere, we can calculate the air temperature which would mean that the atmosphere is saturated//ed = esTw− ϒasp (Td − Tw) Patm(ϒasp=0.0008C-1)

Humidity: the amount of water the atmosphere can ‘hold’. Absolute humidity: the mass of water vapor in a unit volume of air.

Net radiation – is used in heating ….

- Soil{Heat flux, G} - Air{Sensible heat, H} - Water{Latent heat, LE} to evaporate

Latent heat of c and v = +-2500 J.g-1 // LE of fusion =333.688 Specific heat of water = 4.186 J.g-1.K-1

Evaporation – water removed from surface to atm Transpiration – depends on plant physiology and its adaptation to water availability, extracts water over the entire root zone Evapotranspiration - Three major considerations related to mass transport away from the evaporating surface//Energy input: solar energy limitation//Water content: need a supply of moisture//Turbulent transport: need a moisture gradient and mechanism to drive moisture away (wind) Assumption – open water : no water limit, change in volume is measurable, applied to lake, reservoir, streams. PET Assumption - the evaporation rate from a short green crop, completely shading the ground, of uniform height and with an adequate water supply in the soil profile. Important distinction between potential and actual ET:Potential Evaporation (PET)Rate of evaporation that would occur from a uniformly wet, large area completely covered with vegetation and unlimited water supply.Actual Evaporation (AET)AET takes into account water supply limitations at the soil surface and limited supply of water to roots. It represents the true conditions in the land at that time.

T

Tes

3.237

27.17exp6108.0

Cloud formation&Rainfall mechanism

-Turbulace: convection of air(usual resut is a thurderstorm, most eff. Process in RainF.) -Uplift: Orographic cloud -Frontal: movement of one air mass over another. Hot over cold, vice versa. - Convergence: air rise due to low pres.

Air cooling process:

-Radiation of heat outward -Contact with colder mat.,eg fog. -Mixing with colder air

Precipitation measurement

-The simple rain guage {daily}

-Pluviometer {continuous measurement}

Errors: 1. Non-standard collector 2. Initial wetting device 3. Interval during tipping 4. Frictional effect based on weight of collector 5. Wind effect&obstruction 6. Non-vertical setup and Spatial average error

Setup – rain gague density design depends on terrain of the region// flat – fewer//mountainous more gauges needed.

Double mass curve analysis: to eliminate the inconsistency we can change of location, instrument or observational procedure

Radar measurement of Rainfall

-Characteristic of radar -atmospheric condition -distance to precipitation -nature of precipitation -Limit to 200-300km(in grid of 1x1km2)// strength of radar depends on size,conc,shape,state of the precipitation particles.

Mean and Mid Section method:

Catchment Average Rainfall

- Arithmeric mean :-Misrepresent the data, out of boundary. - Thiessen method: Sum{w.Area(i) x p(i)} = P

-Isohyel method

Lecture 4

Model Calibration and validation •Calibration – using the available data to determine model parameters •Validation – looking at the prediction errors from the model Lecture 5 – Rainfall vs Runoff -Rainfall – hyetograph (mm/period) -Runoff – flow, amount of water on the ground -Time variation of runoff – hydrograph (m3/s or ML/day) – volume per time

Crest: Contains the peak flow//Duration at this flow depends on length of time of rainfall//Key for design and forecasting. Falling Limb: Also called the recession Decrease in discharge//Storage in the catchment reaches a peak and then decreases//Only depends on catchment properties – not rainfall Baseflow: Contribution from groundwater to the stream//Is not constant during the storm//Generally removed for design //Design based on surface runoff/direct runoff

Rising Limb: Increase in discharge

Due to gradual filling of storage in the channels and over the catchment surface.

Losses a slower rate of rise

Effect of catchment shape

Effect of antecedent soil-moisture

conditions

• Note: in general, the total excess rainfall should be smaller for dry antecedent conditions

ϕ-Index approach

• Get records of streamflow and rainfall

• Separate baseflow – more on this later

• Sum flow volume over all time steps

• Convert direct runoff to units of depth - CQS

• Guess an initial value for ϕ

• Calculate excess rainfall using this value of ϕ

• Sum over all time steps Σ = CPE

• Repeat for different value of ϕ until CQS = CPE

Calculate total flow volume and convert to depth

• Each time step = 30 minutes = 1800 seconds

• Volume = Σ Qi x 1800

• Volume = 2253894 m3

• Area = 18 km2

• Depth = Volume/Area

• CQS = 125 mm

Day TimeDirect

Runoff

m3/s

24-May 20:30

21:00

21:30 0.0

22:00 15.2

22:30 57.2

23:00 152.5

23:30 260.8

0:00 302.9

0:30 223.6

25-May 1:00 112.5

1:30 53.5

2:00 40.6

2:30 24.2

3:00 9.3

3:30 0.0

4:00

4:30

Guess ϕ – try number 3

• Guess 3 ϕ = 12 mm/hr

• Loss per time step = 6 mm

• Σ = 125 mm (CPE) – OK (CQS = 125 mm)

Calculate sum of excess rainfall

Time RainfallExcess

Rainfall

mm mm

20:30 4 0

21:00 7 1

21:30 34 28

22:00 56 50

22:30 53 47

23:00 5 0

23:30 2 0

Physical approaches

• Horton’s method– Once water ponds at the surface, infiltration starts

at some initial rate (f0) with exponential decrease over time to a constant rate (fc)

– Difficult to calibrate to observable soil parameters

• Phillip’s method– Infiltration rate depends on hydraulic conductivity

(K) and Sorpivity (S) – soil suction potential

– Both parameters can be measured

Green-Ampt method

• Parameters: K, , and θe

• K: hydraulic conductivity

• : soil suction

• : porosity

• θe: effective porosity

• f(t): loss rate

• F(t): cumulative loss rate

e

r

ees

)1(

Effective saturation

Effective moisture content

Residual moisture content

1

)()(

tFKtf