“You’ll find that the only thing you can do easily is be wrong, and that’s hardly worth the effort

”

Norton Juster

The Phantom Tollbooth

U6115: Climate & Water

Friday, July 18 2003

• Water Properties

• Heat capacity, latent heat, saturation vapor pressure, etc…

•Precipitation

•

Condensation, rainfall (spatial & temporal)

• Evaporation

•

Evaporation, transpiration, mass/energy balance

1) 2) 3) 4)

Water – Precipitation/Evaporation

Temporal and spatial change in energy of atmosphere will affect the amount of moisture and thus heat transfer Regional water mass balance will be affected .

Precipitation is primary input of water to a catchment Evaporation is (often) the primary output from a catchment .

Nature and Cause of Floods

The nature of each hydrograph depends upon watershed and storm characteristics  strong relationship between hyetograph (precipitation) and hydrograph (stream runoff): -) The resulting peak in the hydrograph is called a of whether the river actually leaves its banks and causes damage!

-) Background discharge between floods is called flood regardless

baseflow

and is supplied by inflow of groundwaters (Sta Cruz river in AZ)

Nature and Cause of Floods

• in rivers, floods and low flows are expressions of the temporal variability in rainfall or snowmelt interacting with river basin characteristics (basin form, hillslope properties, channel network properties) • flooding may also be the result of sudden release of water from dams or lakes, ice jams • floods cause the biggest natural hazard damage in the US, example: Mississippi flood, 1993; Honduras, Hurricane Mitch

Movement of flood wave

Flood  In an ideal channel (frictionless fluid) flood wave travels with no change However: may be thought as wave that propagates downstream.

a) Mechanical energy is lost (dissipated) due to friction (roughness of bed) b) Water also stored in pools, wetlands, and backwaters, and is subsequently released (delay) Thus magnitude of flood wave is reduced and its transfer is delayed as it travels downstream: Attenuation by friction and storage (normalization is critical practice)

Flood Routing

flood routing: prediction of downstream hydrograph, if the upstream hydrograph is known a) How quickly a flood crest travels downstream b) How the height of the crest changes as it travels downstream flood routing in rivers and by reservoirs dV/dt = I-O Typically, in hydrology problems like these cannot be solved by differentials but must be solved numerically easily.

 transforming the equation into one or more algebraic equations that can be solved more

Flood Routing

Prediction of downstream hydrographs requires a) An estimate of speed of wave crest b) An estimate of the volume added by inflow c) Influence of friction d) A complete understanding of hydrology & hydraulics of drainage basin The 2 most important variables: a) Depth b) velocity dV/dt = I-O Solving this equation requires 2 equations -) statement of conservation of mass -) conservation of momentum Need numerical method to transform DFQ into algebraic one: V n+1 - V n / D t = I n +I n+1 /2 - O n +O n+1 /2

Flood Routing

Reservoirs’ size and volume affect the routing very rapidly. When reservoirs increase in size (and volume)  they store more water and rise in water (h) is smaller  increase in outflow is smaller (delay and reduction of O).

A flood wave in rivers, on the other hand, must move through a long stretch of river before peak discharge is reduced as much as moderate-size reservoirs can accomplish in a relative short distance

Flood Frequency Analysis

simplest approach: use worst event on record * past record key for the future?

Statistical techniques

use the following approach * highest discharges recorded in each year are listed * the floods are ranked according to magnitude, the largest flood is assigned a rank 1, the second largest rank 2, etc The flood statistics are estimated graphically by plotting the logarithm of discharge for each flood in the annual series against the fraction of floods greater than or equal to that flood: r/(n+1) where r is the rank of the particular flood

Flood Frequency Analysis

* The return period, the average span of time between any flood and one equaling or exceeding it, is calculated as T return * The 100 years flood = 1/(exceedance probability).

can then be estimated from the graph * Normal distribution works often well with precipitation data and ln normal for discharge * Problems: not deterministic , based usually on non-adequate data, climate and terrestrial environment is variable

Fate of Precipitation

1) 2) 3) 4) Interception Infiltration Evaporation Runoff Infiltration is influenced by type of soil and vegetation

Evapotranspiration

• evapotranspiration summarizes all processes that return liquid water back into water vapor evaporation : direct transfer of water from open water bodies transpiration : indirect transfer of water from root-stomatal system • water needed as well as solar energy • of the water taken up by plants, through their stomata (only 5% is turned into biomass!) potential evaporation (PE), ~95% is returned i.e. the evaporation rate given an unrestricted water supply - different from actual evaporation to the atmosphere • how can the actual evapotranspiration be measured?

• water balance • energy balance • or combination of both

Evapotranspiration

Apart from precipitation, the most significant component of the hydrologic budget is evapotranspiration . Evapotranspiration varies regionally and seasonally; during a drought it varies according to weather and wind conditions Slightly more than 10% of atmospheric moisture (40,000 bg) is precipitated as rain, sleet, hail, or snow in the conterminous USA. The disposition of this precipitation is illustrated below.

Evapotranspiration:

~

67% (majority of loss through transpiration) Runoff: 29% Groundwater outflow: ~2% Consumption: ~2%

Evapotranspiration

Estimates of average statewide evapotranspiration for the conterminous United States range from about 40% of the average annual precipitation in the Northwest and Northeast to about 100% in the Southwest. During a drought, the significance of evapotranspiration is magnified, because evapotranspiration continues to deplete the limited remaining water supplies in water bodies and soils

Evapotranspiration

Estimation of ET 1) from the water balance

this approach may suffer from the uncertainties in the numbers, example:

dV/dt

=

p

+ r

si

- r

so

-

et

= 0



et

= p + r

si

- r

so

r r p = 10 7 ±5x10 5 si so m 3 /y (±5%) = 10 9 ±1.5x10

8 m 3 /y (±15%) = 9.95x10

8 ±1.5x10

8 m 3 /y (±15%) Here, if we neglect the groundwater inflows and outflows, we can use these values to solve for

et

.

The results, accumulating the errors as we go, is:

1.5x10

7

±3x10

8

m

3

/y

Unrealistic to expect to be able to quantify accurately all terms in a water balance for a catchment to solve for

et

, especially over short periods where storage changes are both substantial and difficult to measure precisely (or predict).

Diagnostic  NOT predictive approach

Evapotranspiration

Estimation of ET 2) from the Energy balance

First Law of Thermodynamics: conservation of energy (E) Thermodynamic principles hold that the net radiant energy arriving across the boundary of a surface land system (including a very thin top soil layer, vegetation, and immediate surrounding air), must be exactly balanced by other energy fluxes across the boundary and the net change in energy held within the volume.

Total incoming E = Outgoing E + any increase in the body’s internal E ( D Q) dQ/dt = R n -G-H-E l Rn = net (solar) radiation G = output (conduction) to the ground H = output (sensible heat) to atmosphere E l = output of latent heat

Evapotranspiration

Estimation of ET 2) from the Energy balance

All matter has internal energy (expressed in calories or joules) a) Specific heat capacity provides a measure of how a substance’s internal energy changes with temperature Cp = (dE u /m)/dT Water has a specific heat of 1.0 cal/g.°C or 4.2x10

3 J/kg.°C b) Latent heat is the amount of internal energy that is released or absorbed during phase change (no change in temperature), at a constant temperature .

l v = 2.5 - (2.18x10

-3 x D T) x10 6 At 20°C  l v = 2.45x10

6 J/kg J/kg

Evapotranspiration

Estimation of ET 2) from the Energy balance

The rate of evaporation can be described, in the context of the energy balance equation, as an energy flux dQ/dt = R n or - G - H - E l E l = R n - G - H - dQ/dt Since the heat flux is related to the rate of evapotranspiration (through latent heat of vaporization)

et

= E l /( r w x l v ) We can then substitute this later equation into the previous one:

et

= (R n - G - H - dQ/dt)/( r w x l v )

Evapotranspiration

Estimation of ET 2) from the Energy balance

When water is in limited supply, the surface becomes warmer than in the wet cases and more energy is removed from the control volume through conduction in the the soil and heating of the air.

In this case the surface properties, rather than the atmospheric conditions, are controlling the rate of evapotranspiration. (eg. Higher winds and lower saturation will increase evaporation rate, while reduced solar radiation - clouds - will reduce evaporation)

Evapotranspiration

Estimation of ET 2) from the Energy balance

Relationship between surface wetness and the partitioning of received energy between evaporation and heating of air and soil

Evapotranspiration

Estimation of ET 2) from the Energy balance

The rate of

et

that occurs under prevailing solar input and atmospheric properties, if the surface is fully wet , is commonly referred as

Potential Evapotranspiration

(PET).

For a catchment water balance, we are interested in the actual

et

(rate at which water is actually removed).

When a surface is wet

et

/PET = 1, when it is dry

et

/PET ~ 0

Dams Reasons for dams building: 1) Water storage: “stable” source in water quantity 2) Reduction in flood risks 3) Source of energy (hydroelectricity) 4) Recreation 5) Fire and farm ponds 6) Irrigation (similar to #1) 7) Waste disposal (mining, livestock) 8) Navigation

Dams The US now has the capacity to store the equivalent of almost a full year’s runoff in reservoirs behind ~ 80,000 structures

Dams Dams ownership and function:

Dams Dams distribution in the US: (National Inventory of Dams – USACE)

Colorado River hydrograph

Questions:  When does discharge peak and why?

 The hydrographs were taken at different locations of the river, what is the difference in the hydrographs and why is there one?

 

Colorado River hydrograph

Hydrographs are variable between years Discharge often peaks in late winter or spring, snowmelt

Discharge - Colorado River

140000 120000 100000 80000 60000 Discharge 40000 20000 0 10 /1 /1 92 1/ 1 1/ 19 22 4/ 1/ 19 22 7/ 1/ 19 10 22 /1 /1 92 1/ 2 1/ 19 23 4/ 1/ 19 23 7/ 1/ 19 10 23 /1 /1 92 1/ 3 1/ 19 24 4/ 1/ 19 24 7/ 1/ 19 10 24 /1 /1 92 1/ 4 1/ 19 25 4/ 1/ 19 25 7/ 1/ 19 10 25 /1 /1 92 1/ 5 1/ 19 26

Date

Colorado River hydrograph



Reservoirs smooth out extremes

Discharge - Colorado River

140000 120000 100000 80000 Discharge 60000 40000 20000 0 10 /1 /1 92 10 1 /1 /1 92 10 6 /1 /1 93 10 1 /1 /1 93 10 6 /1 /1 94 10 1 /1 /1 94 10 6 /1 /1 95 10 1 /1 /1 95 10 6 /1 /1 96 10 1 /1 /1 96 10 6 /1 /1 97 10 1 /1 /1 97 10 6 /1 /1 98 10 1 /1 /1 98 10 6 /1 /1 99 10 1 /1 /1 99 10 6 /1 /2 00 1

Date



Colorado River

Role of floods on ecosystems

Dams generate 1) Reduction in sediment load Factors that control sedimentation • Relationship between average grain size and energy of bottom currents

Dams

• • Erosion, Transport and Deposition (sedimentation) depend on velocity of current and grain size Settling rate of suspended particles varies with diameter (Stokes Law)

Dams

Dams provide 1) “Stable” source in water quantity 2) Reduction in flood risks 3) Source of energy (hydroelectricity) Dams generate 1) Reduction in sediment load 2) “Questionable” source in water quality (eutrophication, metals, etc) 3) Reduction in water flow to coastal systems (Rio Grande, Colorado) 4) Source of GHG (hydroelectricity) 5) Impact on ecosystems (Hg, biodiversity) Reasons for removal 1) Structural obsolescence 2) Safety and Security 3) Recreational oportunities 4) Water quality and quantity issues 5) Ecosystem restoration (and species protection)

Dams Dams removed in the US: (National Inventory of Dams – USACE)