Hydrological Concepts and Physical Properties of Water
EESB04 – Review Lecture 2: Hydrological Concepts and Physical Properties of Water - What is Hydrology? - Delineating a watershed - Water balance: ∆S = In – Out - Measuring rainfall - Spatial Variability – changes over space - Temporal Variability – changes over time - Residence Time (TR) =
=
(assuming input = output)
- Spatial distribution of Water - The Hydrological Cycle 1) The land receives more precipitation than evapotranspiration 2) Oceans evaporate more than it receives precipitation 3) Excess of water on land returns to oceans as runoff, which balances #1 and #2 - Principle driving forces of the Hydrological cycle: Solar energy and gravity - Spatial variability in global precipitation (the “middle finger” graph) - Spatial variability in global evapotranspiration - Spatial variability in global run off - High precipitation + low evapotranspiration = high runoff - Low precipitation + high evapotranspiration = low runoff - Hydrological Models - Empirical – statistical relationships, not robust - Deterministic – known physical relationships, more robust - Stochastic - statistics - Typical Hydrological Model Structure - Basic models: inputs model outputs - Complex models: outputs may be used for inputs for another model - Typical inputs and outputs - Sensitivity Analysis - Small change = not sensitive, big change = sensitive - Models are made for relative comparisons, and variables with no sensitivity are insignificant in the model - Physicochemical Properties of Water - Molecular structure of water - 3 States: solid, liquid, gas - Hydrogen bonding, strong covalent bonds between O and H - Without H-bonding, water would be a gas (water vapour) at room temperature - Asymmetric structure - 105° angle between the 2H’s in H-O-H - Surface tension, an electrochemical attraction because of hydrogen bonding
- Capillarity – the upward movement of water, due to effects of wetting and surface tension - Meniscus - The smaller the diameter, the further water can travel up a tube - Phases of Water (remember the terms and molecular structure) - Liquid (Water) and Solid (Ice) – freezing and melting - Liquid (Water) and Gas (Water vapour) – vaporization/evaporation and condensation - Gas (Water vapour) and Solid (Ice) – sublimation and sublimation - Sublimation – solid turning into gas (and vice versa) without becoming a liquid - Why do ice cubes float? - Water density maximum is 1.00g/cm3 at 4°C - When temperature drops below that, water becomes less dense and forms hexagonal crystals of ice (less dense), therefore ice floats - Density of Water - Water contracts as it cools, but only to a point at 4°C - Beyond 4°C, water expands as more H-bonds form hexagonal structures until -29°C - Phase Changes - Heat energy is either absorbed or released to change from one phase to another - Amount of heat energy required to break the h-bonds - 1 calorie = 4.184 J (joules) - Ice Water Water Vapour – latent heat is absorbed to break h-bonds - Water Vapour Water Ice – latent heat is released to form h-bonds - Latent Heat (2 types) - Latent heat – involved in phase changes of water - Sensible heat – heat that you “feel” or “sense” Lecture 3: The Energy Balance and Water in the Atmosphere - Radiation – energy in the form of waves and sub-atomic particles - Planck’s Law – wavelength of energy emitted by a surface decreases as temp increases - Wien’s displacement law – calculates wavelength at which max energy radiation occurs - λmax =
T = temperature (in Kelvin)
- The electromagnetic spectrum - Shorter λ = blues, violets - Longer λ = reds - Energy pathways and principles - Driver of energy on Earth is radiation from the Sun - Drivers of spatial & temporal variation: seasons, latitude, clouds, surface characteristics - 1 µm = 1.0 × 10-6 m - Insolation = INcoming SOLar radiATION - It is shortwave radiation (inputs are UV, visible light, near-infrared wavelengths) - Energy outputs from Earth
- Surface Radiation Balance - Direct vs. Diffuse radiation - Shortwave vs. Longwave radiation - Water vapour the most dominant GHG, absorbs Earth’s long λ - GHG increase absorption of energy, not necessarily more reflectivity - Measuring energy depends mostly on the surface temp of the body emitting it - Wien’s law = what type of energy - Stefan-Boltzmann law = how much energy moved per area per unit time - QR = ƐσT4 - Blackbodies – 100% efficient in emitting energy (Ex. Sun, Earth) - Darker things tend to have higher Ɛ, lighter things have a lower Ɛ - Solar constant - Sun’s energy arrives at edge of atmosphere at an average of 1.74 × 1017 W - Area of Earth is 1.28 × 1014 m2 - Isc = Sun’s Energy / Area of Earth = 1367 W m-2 Solar Constant - Energy Balance (Fig. 3.2 slide 17) - About ½ of the energy received at the top of the atmosphere is absorbed by the Earth - Clouds and atmosphere play a role in absorption and reflection - Outgoing energy + Incoming energy = 100 (100 units represents the solar constant) - Albedo – determines the ability of a substance to reflect energy - Albedo = reflecting radiation / incoming radiation α = ↑K/↓K - Albedo of water extremely variable because of surface, angle of incoming radiation, etc. - Smooth surfaces increase α while rough surfaces decrease α - Incoming radiation (energy) is absorbed, moved around (spent) as sensible energy - Radiation balance (Q*) - Short λ energy balance = incoming short λ – reflective short λ K* = K↓ - K↑ - Reflective short λ = albedo × incoming short λ K↑ = αK↓ - Long λ energy balance = incoming long λ – reflective long λ L* = L↓ - L↑ - Radiation balance Q* = K* + L* (net radiation) - 24 hour Q* graph - Heat Transfer at Earth’s surface by several processes - Conduction – molecular transfer - Convection – heat transfer by vertical movement - Advection – heat movement of liquid or gas horizontally - Expenditure of Net Radiation (Q*) - 3 ways that net radiation is expended from a surface: LE, H, G - Latent heat of Evaporation (LE) – energy stored in water vapour as water evaporates - Sensible Heat (H) – back and forth transfer between air and surface via convection and conduction - Ground heating or cooling (G) – energy flowing through ground only via conduction
- Relationship between Net Radiation (Q*) and Expenditure of Net Radiation - We already know that Q* = K* + L* - Expenditure Q* = ∆LE + ∆H + ∆G - So therefore, K* + L* = ∆LE + ∆H + ∆G - Partitioning of LE and H - Main factor is available moisture - A system that is moist will use more latent energy - A system that is dry uses more sensible energy (less water to evaporate) - Review the example of you being at the shore vs. in the middle of the lake! - Bowen Ratio – describes type of heat transfer in a water body -
-β=
β > 1 = more H than LE, β < 1 = more LE than H
- Importance of Precipitation - Latent energy a driving force for evaporation and precipitation - Rain and snow are main hydrological inputs to the surface of the Earth - Precipitation a major control on vegetation and ecology - Understanding precipitation inputs is critical (ex. Planning purposes) Lecture 4: Precipitation and Interception - Forming Precipitation (3 processes must occur) 1) Cooling to the dew point 2) Condensation onto nuclei 3) Droplet growth - For precipitation to occur for any appreciable time, this 4th process must occur 4) Importation of water vapour (ex. hurricanes suck in so much air which leads to more precipitation) - Cooling to the Dew Point - Dew point – the temperature at which a given parcel of air becomes saturated - Condensation occurs when air parcel cooled beyond dew point or if moisture is added to an air parcel already at dew point - Vertical uplift the common means of cooling air, results in adiabatic cooling - Adiabatic Cooling - The cooling of an ascending air parcel without heat exchange between the parcel and surrounding air mass - Air parcel expanding as it rises because less pressure - Review the 4 key points of air parcel and adiabatic cooling (slide 31) - Dry (DALR) vs. Saturated (SALR) Adiabatic Cooling - DALR: 1°C / 100 m (when parcel of air < saturated vapour pressure) - SALR: 0.5°C / 100 m (when parcel of air ≥ saturated vapour pressure) - Review the Saturation Vapour Pressure graph - Saturation Vapour Pressure – the pressure exerted by water vapour molecules in the air when air is saturated with water vapour
- Lifting Mechanisms - Adiabatic cooling of air parcels require “uplift” - Mechanisms of uplift: - Convectional lifting – air rises by local surface heating, short intense storms - As warm air rises, other air takes its place - Orographic lifting (topography) – topographic barrier force air to rise, chinooks - Frontal lifting (convergence) – contrasting air masses converge with warm air rising over cold - Cold front – cold air mass moving into warm air mass, short violent precipitation Ex. large raindrops, heavy showers, lighting, thunder, hail - Warm front – warm air mass moving into cold air mass, longer duration drizzly shower - Condensation - Need cloud condensation nuclei (CCN), particle impurities in atmosphere > 10-4 mm - When dew point is reached, CCN provides surfaces on which water can condense - “Cloud seeding” (silver iodide) - Droplet Growth - Droplets in cloud (0.001-0.02 mm) must grow to about 0.4 – 4 mm - This happens through drop collision, coalescence or ice-crystal growth - 2 reasons for droplets not reaching the ground: Evaporation or Friction - Warm clouds (temp > 0°C) - Collision-coalescence process – turbulent mixing of droplets cause collision and growth - Creates light drizzle, primary mechanism in tropical regions - Cold clouds (temp < 0°C) - Super-cooled water – liquid water chilled below freezing point without becoming solid - Bergeron-Findeisen Process - Importation of Water Vapour - Concentration of liquid water in most clouds only 0.1 – 1 g m-3 - Not enough water in most clouds to produce significant rain, water vapour needs to be continually added into clouds - Winds converging provide a source of moisture - Important Precipitation Parameters - Type – rain, snow, hail, sleet, etc. - Depth – expressed in mm - Duration – how long - Intensity – rate of precipitation over a period of time (mm/hr) - Return Period – likelihood a given precipitation even will occur - Influences on Precipitation Distribution - Static influences – altitude, aspect, slope - Dynamic influences – source of water, variations in surface water temp, convectional uplift mechanisms
- Impact of Altitude – Rainshadow effect - Chinook winds – warm dry downward sloping air caused by adiabatic warming - These warm winds lose its moisture on the downward slopes, can make snowmelt - Minor impact of slope and aspect on measuring precipitation - Interception – interception of precipitation by vegetation or buildings - 10-40% (average) of gross precipitation is lost to interception loss - Interception loss – precipitation intercepted by vegetation that evaporates back into atmosphere - Interception Processes - Gross rainfall (R) – rainfall measured above vegetation or in the open R = Rt + Rs - Interception (I) – storage of precipitation on surfaces where it is subject to evaporation - Throughfall (Rt) – rainfall that reaches the ground passing through canopy - Stemflow (Rs) – water that reaches the ground from running down trunks or stems - Canopy Interception Loss (Ec) – water that evaporates from canopy - Litter Interception Loss (El) – water that evaporates from ground surface (litter, leaves) - Total Interception Loss (Ei) = Canopy loss + litter interception loss Ei = Ec + El - Net Rainfall (Rn) = Gross rainfall – Total Interception loss Rn = R – Ei = (Rt + Rs) – (Ec + El) - Net vs. Gross precipitation - Net precipitation – what actually gets to the ground - Gross precipitation – the total precipitation - Leaf Area Index (LAI) – the ratio of leaf area to ground surface area - LAI > 1, more than 1 layer of leaf per ground area, more likely to intercept (but throughfall can also occur indirectly if canopy storage capacity is exceeded) - LAI < 1, there are openings in the canopy to allow direct throughfall - Funneling effect of Interception - Deciduous trees grow like a “funnel” and have substantial infiltration of water into the ground at the stem and outside of canopy cover - Stemflow in most systems often less than throughfall - Stemflow - Often not well measured - Best measurement procedure is to directly measure all trees within a plot 1.5x the diameter of the largest tree’s crown in the plot - Create an eavestrough, wrap around bark at least once, collect water in can to be weighed - Coniferous vs. Deciduous tree interception - Coniferous intercept 10-15% more than Deciduous on an annual basis - Deciduous trees lose their leaves, but during growing season they are equal - Also depends on the season, coniferous trees can hold snow (makes a big difference) - Canopy structure makes a big difference, pine (needles) vs. fir-hemlock (dense leafing)
- Factors affecting Interception - Vegetation type, time of year, and size affect interception - Measure Leaf Area Index (LAI) to explain these effects - How precipitation falls (intensity, duration, frequency, etc.) is a major control o Intensity: more intense = less interception o Duration: longer = less interception o More frequent = less interception - Wind affects evaporation and interception, snow is easily intercepted but can be blown off by wind as well - Measuring rainfall depth - Rainfall depth – the real depth of a layer of water on a flat impermeable surface after rainfall - Recording rain gauge – device that measures rainfall intensity - Rainfall intensity – rainfall measured in a short period of time (mm/hr) - Precipitation Gauge types - Weighing raingauge - Float and Siphon - Tipping bucket - Measurement Accuracy – many factors affect precipitation measurement accuracy - Orifice (opening) size - Orifice orientation – flat, facing a slope, horizontal rainfall - Orifice height (from surface) and shielding – the higher the more windspeed - Nearby obstructions – must be well-exposed, avoid rainshadows - Splash, evaporation, wetting losses, snow blown off by wind - Good practices to prevent problems of measurement inaccuracy (Pg. 30) - Shielding reduces turbulence - Setting up apparatus, you want the distance of the raingauge from obstructions to be 2x the height of obstructions - Areal Estimation of precipitation – point measurements in a region as area estimates of precipitation for an entire region (such as watersheds) - Arithmetic average - Thiessen polygons - Hypsometric method - Isohyetal method – good for cases when majority of rainfall takes up a watershed Lecture 5: Rain and Snow - Review sample exam questions at beginning of lecture slides - The Importance of Snow - It stores water over several months and then releases it quickly (on average 150 mm) - Snow and glacier melt a major source of fresh drinking water
- How does snow fall? - Instead of condensation, water vapour undergoes sublimation - Sublimation – rising air (100% saturated) reaches its frost point (temp ≤ 0°C), and the water vapour in that air parcel changes to ice without passing through liquid state - Snow falling is crystalline, and snow accumulating on ground becomes granular - Warm clouds – rain comes down as rain (never snow!) - Cold clouds – snow remains cold and falls as snow (when heavy enough), and it remains as snow if it hits a cold ground - Snow Hydrology terms - Snowfall – depth of solid precipitation on surface over a time period - Snowpack – accumulated snow on the ground at time of measurement - Snow water equivalent (storage term) – total volume of liquid water that would result from melting a snowpack over a given area (ex. depth) - Snowmelt – depth of liquid water produced by melting that leaves the snow pack over a time period - Ablation – total loss of water (depth) from a snowpack over time Ablation = snowmelt + evaporation/sublimation - Water output – depth of liquid water (including rain on snow) leaving a snowpack over a time period - Porosity (Ф) – volume of air and water over the total volume of the snowpack Ф= -
Liquid-water content (ʘ) – the ratio of water to total volume ʘ=
- Snow water equivalent Height of melted water =
× height of snow hm =
hs
- Snowpack changes over time - Freshly fallen snow has a density ratio (ρs/ρw) between 0.004 to 0.34 Once deposited, 4 metamorphism mechanisms make it more dense until melt is complete: 1) Gravitational settling – settling increases due to weight of overlying snow, and temperature of that layer 2) Destructive metamorphism – snowflakes evaporate and vapour deposits on surfaces creating larger, spherical snow grains - As melting occurs, snowflakes become more dense and have less air space in between 3) Constructive metamorphism – most important pre-melt densification process in seasonal snow (Review slide 19) - Sintering – two snow grains touch build a “neck” between adjacent grains as some melted waters re-freeze - Sublimation can occur in warmer sections, and vapour moves toward cooler spots where condensation occurs
- Depth hoar – snow near base sublimates at a high rate, leads to basal layer of large planar crystals low in density and strength 4) Melt metamorphism 1) Liquid water at surface freezes in cold snowpack, making it more dense (layers of solid ice) 2) With the presence of liquid water, smaller snow grains disappear and larger ones (sand size) dominate - As snow melts over time, these 4 mechanisms may occur until the snow fully melts - How does Snow Melt? - Melt starts to occur when net input of energy into the snowpack turns from – to + - 3 Important stages of snowmelt (important for exam!) 1) Warming phase 2) Ripening phase 3) Output phase – you only see water come out at this phase! 1) Warming Phase: - The phase when snowpack temperature increases steadily until it is “isothermal” at 0°C - Cold content (Qcc) – the amount of energy required to raise the average temperature of a snowpack to the melting point (0°C) - Qcc = -ci × ρw × hm × (Ts – Tm) 2) Ripening Phase: - The phase where melting occurs and the build up of liquid water up to the point (max) where it leaves (the output phase) - At the end of this phase, snowpack is “ripe” because isothermal at 0°C, cannot retain any more liquid water - Liquid water retaining capacity: hwret = Ɵret × hs - Total energy required to complete ripening phase: Qm2 = hwret × ρw × λf = Ɵret × hs × ρw × λf 3) Output Phase: - The phase when more energy inputs into the snowpack result in water leaving the snowpack - Total energy required to complete output phase (Qm3) = amount of energy needed to melt snow remaining at the end of the ripening phase Qm3 = (hm – hwret) × ρw × λf this equation is missing time - Estimating Snow Loss by Melting Measure water output: -∆hm =
= ∆w
- Alternative Method for Estimating Melt Water: Degree Days - An EMPIRICAL method, best used during overcast periods - M = K (Ta – Tb) - Measuring Snowfall using gauges: Nipher Snow Gauge - Used to capture snow and measure its water content in mm - It is mounted on a sliding metal pipe, so when snow accumulates, it can be raised to keep top edge 5ft above the surface of the snow (prevents ground snow from drifting in)
- The Easy way to measure snow (Manually) - Measuring the snowpack: Stakes: - Stakes driven into the ground surface before winter, and monitored at regular intervals - Density usually assumed Survey: Use a snowcore, stick it into the snow to find depth and to measure volume Use of fish scales to measure weight hm = hs Snow Pillows: - A device used for measuring snowpack, made of glycol or fluid-filled rubber pillow that will not freeze - It measures the water equivalent of the snowpack based on hydrostatic pressure created by overlying snow - Its large size (1 – 4m diameter) minimizes any discrepancy due to bridging of snowpacks Lysimeters: - A measuring device which can be used to measure the amount of actual evapotranspiration (which is released by plants, usually crops or trees) - It records amount of precipitation that an area receives and the amount lost through the soil, which allows you to calculate amount of water lost to evapotranspiration Lecture 6: Evapotranspiration - What is Evapotranspiration? - The sum of evaporation (oceans + land) and plant transpiration from the earth’s surface to the atmosphere - ET controls water vapour in the atmosphere, which controls climate and how to understand climate change - ET the 2nd most important flux, precipitation is 1st, forms balance in hydrological cycle - Evapotranspiration – the net loss of water through the sum of evaporation and transpiration - Evaporation – net loss of water from a surface due to change in liquid to vapour, and net transfer of the vapour to the atmosphere - Transpiration – net loss of water from within the leaves of plants through stomata - You need energy to change the phase, and some sort of force to move the vapour away - Evapotranspiration in the Hydrological Cycle - 62% of Precipitation on land is lost to ET, 112% of precipitation on oceans is lost to ET - Factors required for Evaporation 1) Available energy 2) Available moisture (Ex. In the desert there is little to no evaporation) 3) Capacity for water vapour in the atmosphere (if no capacity then no movement)
1) Available Energy - Main source of energy for ET is from the Sun - It is the net accumulation of energy at the surface (Q*) Q* = QS ± QLE ± QG - When water moves from liquid to gas, energy is absorbed, so QLE is a negative flux Lesser forms of Available Energy 1) Anthropogenic Energy – things like heating of houses or heat produced by vehicles 2) Advective Energy – horizontal flux of energy (often latent energy) blown from far away 2) Available Moisture - “Open” water (ex. lakes, ponds) evaporate more freely, denoted by Eo - Soil surfaces have smaller supply of available moisture, and as surfaces dry out, it becomes more difficult to “pull” water up against forces of gravity and tension Lecture 7: Evapotranspiration (Continued) and Soil Water - AET vs. PET - PET (Potential Evapotranspiration) – the amount of ET that would occur if water were NOT limiting (Ex. lakes) - AET (Actual Evapotranspiration) – the actual amount of ET that occurs whether water is limiting or not - Lakes evaporate at a potential rate, soils do not evapotranspirate at a general rate - AET difficult to measure, PET generally used for measurements (but need caution!) - The Receiving Atmosphere and Gradients - Like many physical processes in the environment, ET driven by gradients - Fick’s First Law of Diffusion relates diffusive flux to the concentration, postulating that the flux goes from regions of high concentration to low concentration -
Jj = -Dj
- Water in the Atmosphere: Vapour Pressure - Evaporation affects and is affected by amount of water vapour in atmosphere near the evaporating surface - Vapour Pressure (e) – the “partial pressure” of water vapour - Saturation Vapour Pressure (e*) – the max vapour pressure that is thermodynamically stable (function of temperature) - Vapour Pressure Deficit = e* - e (there needs to be a deficit for any movement) - Saturation Deficit of Overlying Air Controls Vapour movement - Evaporation is proportional to es* - ea (vapour pressure deficit) - Equilibrium would be reached quickly and evaporation would stop if not for wind - Therefore, 2 main controls on the rate of evaporation from an open-water surface: 1) Windspeed (controls air turnover) 2) Vapour Saturation Deficit (controls uptake) - Humidity - It is a term for water vapour in the air, not “moist” air - It is measured in different units, and measured using a psychrometer
Absolute Humidity – the actual amount of vapour in the atmosphere (this really IS vapour pressure) - Relative Humidity – the percentage saturation of an air parcel at a specific temperature RH = e/e* × 100 (%) - How a psychrometer works (Review slide 21) - Vegetation Canopy ET - Evapotranspiration at top of vegetation canopy is a mix of: 1) Evaporation from soil 2) Transpiration from leaves 3) Interception loss - Transpiration - Water leaves stoma because of vapour pressure gradient results in a “pull” from the roots out the leaf - Mechanisms to reduce transpiration: leaf wilting/curling (reduces leaf area), alteration of orientation to sun energy, closure of stomata (caused by plant wilting) - Interception Loss - Biggest influences 1) Canopy structure 2) Meteorology (atmospheric conditions) - Canopy Structure 1) Storage capacity 2) Drainage characteristics (ex. Rhubarb) 3) Aerodynamic roughness (turbulence induction) - Meteorology 1) Rainfall characteristics (intensity, duration, frequency) - Measuring PET and AET - PET measured by pan evaporation, ET gauge - AET very difficult to measure - Direct Micro-Meteorological Methods - These methods attempt to directly measure how much water is evaporated above a surface - 3 main methods: 1) Eddy correlation 2) Aerodynamic profiling 3) Bowen ratio - Spatial scales are generally small - Mostly used for calibration of estimation methods 1) Eddy Correlation – measures and calculates vertical turbulent fluxes within atmospheric boundary layers -
-
E=
× ua’ × q’
2) Aerodynamic Profiling – calculates the energy available for evaporation - Require vertical humidity gradients (humidity and temperature) - Assumes atmosphere is neutral and stable (not always the case) 3) Bowen Ratio – Measuring H (sensible heat) and LE (latent heat energy) is difficult, but it is relatively easy to estimate the H/LE (Bowen ratio β) - More relaxed atmospheric assumptions -
β=
=
E=
- Water Balance Approaches - Try to solve for ET in the water balance - Often, everything BUT evapotranspiration is measured, so there may be many errors - Principle approaches: 1) Evaporation pan 2) Lysimeters 3) Soil water depletion over time 4) Watershed water balance 1) Evaporation Pan Approach: E = ceEp (Ep = ∆S – P) 2) Lysimeters – use an isolated plot that is under the same conditions as surrounding area - Conduct a water balance dominated purely by irrigation and ET - Best way to measure ET, but very expensive (worth 4 houses) - Often used to make a pan coefficient 3) Soil Water depletion over time - Need to monitor VMC of soils between periods of time under relatively strict conditions: - Water table considerably deeper than root zone - Easiest when runoff and drainage are ZERO 4) Water balance approach AET = P = Q ± ∆G ± Ɵ, and over a long period potentially: AET = P - Q - Generally used at large scale (watershed) - Errors with certainty of these variables can be up to 50-100% - Empirical/Theoretical Estimation - These techniques use climatological variables known to influence ET and uses them to stimulate ET most estimate PET (potential evapotranspiration) - 2 Popular Approaches: 1) Thornthwaite Method 2) Penman and modified approaches (more approaches AET) - Thornthwaite Method - This method is for monthly ET only, and highly EMPIRICAL - Calibrated for humid temperate regions - Need only mean monthly temperature (T) and latitude
-
]a
Etp = 16b [
- This takes into consideration the energy available of evapotranspiration of water - Thornthwaite Heat Index I=
1.514
a = 6.7 × 10-7I3 – 7.7 × 10-5I2 + 0.018I + 0.49
-
This is empirical and not accurate because “a” is “fudged”
-
To calculate “b” b =
×
(24)
- Penman-Monteith Equation (Slide 16) - Deterministic, physically-based model for evaporation that includes both the energy required to evaporate water and the atmosphere’s ability to receive vapour - Takes into consideration biotic control (resistance) Ea =
×
Simplified: Ea = 0.408 ×
∆=
- Aerodynamic Resistance (ra) - It is the resistance (inverse of conductivity) encountered by water vapour in diffusing into air from a surface (vegetative or open water) - It is reciprocal to the roughness of the earth’s surface and wind speed near surface Ex. Rougher surface + stronger surface winds = more turbulent mixing + less resistance to evaporation - “Unstressed conditions” (AET = PET), ra decreases with roughness - Surface Resistance (rs) - It is a physiological resistance imposed by vegetation stomata on the movement of water vapour by transpiration - It is variable in relation to moisture availability (Ex. Open water = 0 s m-1 b/c no limit) - “Unstressed conditions” then Penman-Monteith solves for PET - Surface resistance opposite to Aerodynamic resistance: high rs low ra, low rs high ra - The difficulty of Modeling - ET calculated by Penman-Monteith is sensitive to resistivity terms, which are difficult to accurately parameterize - Often Penman-Monteith only useable in research situations - Estimations often applied through Reference Crop Evaporation approach - Reference Crop ET – based on ET from an “idealized” surface - A grass crop with uniform height and specific features: 12 cm high, albedo of 0.23, and surface resistance of 69 s m-1
- Reference Crop Evaporation - Reference crop evaporation (given ra and rs) are multiplied by a “crop coefficient” (Kc) for a particular crop to arrive at PET - Kc changes with different growth stages of a crop, it is not a constant - Ra calculated for the reference crop as 208/u2, where u2 is wind speed at 2m height Ep = Kc × Erc - Where is water “stored”? - Water hits the ground and infiltrates into the soil water (unsaturated) and groundwater (saturated) - Soil is not really a barrier, it has particles and air spaces - The smaller these air spaces (pores) the more capillary action - A zone that has all its spaces taken up by water is “fully saturated” - The water table is the boundary between soil water and groundwater - Soil is Beneath us, What is it? - They contain pore spaces with different structures, porosity, and permeability - Sand – macropores, many large spaces (lower porosity, higher permeability) - Clay – micropores, many small spaces (higher porosity, lower permeability) - Soil descriptors: Particle size - Clay = 0.0002-0.002 mm, Silt = 0.002-0.02 mm, and Sand = 0.02-2.0 mm - Soil descriptors: Texture - Many different mixtures of the above 3 give you different porosity and permeability Ex. Loamy Sand, Clay Loam, etc. - Soil Matrix: Air, Water, Soil - Total volume = volumeair + volumewater + volumesoil Vt = Va + Vw + Vs - Vv = Va + Vw -
Porosity = (volumeair + volumewater)/total volume
=1-
=n
- Volumetric Soil Moisture -
Volumetric Moisture Content (water content) Ɵ =
Ɵv =
- This will always be equal or less than porosity - 1000 cm3 = 1 kg - Characteristics related to Soil Mass - Total mass of soil mt = ma + mw + mt - Gravimetric soil water content Ɵg = -
Bulk Density =
ρb =
- Infiltration of Rain and Melt Water into the Ground - Infiltration – the passage of water through the surface of the soil, via pores and small openings, and into the soil profile - Fundamental interface process between atmosphere and lithosphere
-
Highly dependent on soil characteristics, sustains plant growth, recharge groundwater, decreases runoff and erosion, retards (slowing) pollutant transfer to surface water - Infiltration - 2 Principles affect downward movement of water in soil profile (percolation) 1) Tension forces (suction, matric, capillary), directly related to h-bonding between water and walls of soil pores 2) Gravitational Forces - Infiltration terms: - Infiltration rate – rate of water entering soil (mm/h) - Water input rate – rate at which water arrives at the surface (ex. rainfall intensity) - Infiltration capacity – max rate at which infiltration can occur for a certain condition - Depth of ponding – depth of water standing on surface - Factors that affect infiltration – review Slide 35 Lecture 8: Soil Water Zone, Infiltration, and Percolation - Pressure/Tension in the Soil Water (Unsaturated) Zone (also called Vadose Zone) - Pores spaces in an “unsaturated” zone have a NEGATIVE pressure (meaning less than atmosphere pressure) - Negative pressure is “matric potential” or “matric suction” - Matric potential has a negative sign, but matric suction is the absolute value of matric potential - Soil Water Tension - Adhesion – attraction of water to sides of a pore - Cohesion – attraction of water to water - The smaller the radius of the pore, the larger the potential (more suction) - Moisture and Tension - Suction in smaller pores > larger pores - Suction in drier pores > wetter pores - When dry soil is wetted, smaller pores fill first, drainage is first from larger pores - Physical Measurement of Tension - Tensiometer – an instrument used to determine matric water potential (Ψm) (soil moisture tension) in the vadose zone (unsaturated zone) - Soil Moisture Characteristic Curve - Pore size distribution differs between soils - Relation between volumetric soil moisture (Ɵ) and suction (-Ψ) also differ between soils - When you’re wetter, matric suction goes down - Relationship is NOT linear, not as simple as y = mx + b - Sand is well-sorted, suction initially “drops off” (like a “jump”) and then levels off - Clays have significantly higher suction, and also higher volumetric moisture content - Clay is very porous, so VMC is high, but water does not move very well
- Soil Water Classification - Hydroscopic water – water permanently attached to outer edge of a piece of soil o Impossible to get off unless dried or evaporated o This water is not available to plants, plants do not have enough suction power - Capillary Water – water held by adhesion/cohesion o Important for plants, plants have slightly higher power to obtain capillary water - Gravitational Water – excess of capillary water o Any water excess of Field Capacity is excess gravitational water - Field Capacity – max VMC (Ɵ) that a soil can hold against gravity - Wilting point – VMC (Ɵ) at which plants can no longer extract water from soil - This is no longer gravitational water; it is water that plants can no longer obtain - Clay = high FC and WP - Sand = low FC and WP - The area with the most available water is between FC and WP, tend to be loamy soils - “Available” Water - Typical soil has FC at pF = 2.0, and WP at pF = 4.2 (pF = log (suction –Ψ)) - Therefore, available soil water for plants is between pF = 2.0 and pF = 4.2 - Water held between pF = 0 and pF = 2.0 will drain (VMC 30-40%) - Water between 0-10% VMC will not move - Saturation occurs at pF = 0, which is around 42% porosity - Seasonal Changes in Soil Water Storage - Spring, lots of snowmelt and excess water above FC - Summer, plants suck water and transpire alot of water, so percolation water is drained, more sucking and transpiring than water coming in - Fall, loss of leaves and plants die, transpiration decreases and less sucking of water, therefore water content begins to increase again - Summer = deficit, Fall = recovery - Drying and Wetting: Hysteresis (Study the graph for the EXAM!) - What is going on between Drying curve and Wetting curve? - Soils are not drying as much in relation to wetting at higher VMC because dry soils stay wetter at that stage, large pores drain first while smaller pores drain last - Hysteresis – “Ink Bottle” Effect and Contact Angle - Water content stay higher longer when draining in hysteresis - “Bottle neck” holds water by hydrogen-bonding which results in higher water content on draining over time - Meniscus appears because of h-bonding on sides, but gravity pushing it down - Flow in the Unsaturated Zone - 2 Things determine how much water goes through at a time 1) Gradient Pressure – water always move from high pressure to low pressure
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2) Saturated Hydraulic Conductivity – max rate at which water can physically move through soil Water is more easily moveable in wetter soils than drier soils
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Darcy’s Law: q = -K(Ψ)
Q = -kA
- Upward Flow: Capillary Rise - Capillary Rise – the sucking up of water from below through capillary forces - Leads to “Capillary Fringe” – the subsurface layer above a water table in which groundwater seeps up by capillary action to fill pores - Its height limited by air-entry suction of the largest prevailing pore size above water table - Downward Flow: Infiltration & Percolation - Infiltration – passage of water through the surface of the soil, via pores or small openings, into the soil profile - The initial time that water goes through the surface, how quickly depends on suction - Percolation – the downward movement of infiltrated water - Dry soils initially pull the water, then gravitational forces moves it downward - Infiltration – review slides, this was mentioned in previous lecture - 2 Principle factors affect percolation: tension forces, and gravitational forces - Physical Measurement of Infiltration - One easy way is to input water as water is draining out to maintain a balance, then measure the input water rate - Numerical Estimation of Ponded Infiltration: Green Ampt Equation (Skip!) Lecture 9: Soil Water (Continued) and Groundwater - Zero Flux Planes - After rainfall, infiltration continues, but at the same time water above it also evaporating - These two processes meet in the soil profile and creates a “no flow” situation, also known as a “Zero Flux Plane” or “Divergent Zero Flux Plane” - Typical in spring through summer - Autumn, P starts to exceed ET again, surface layers get wetter, “convergent zero flux plane” develops - Zero Flux Plane graph (review the graph) - Percolation through Soil Horizons - Soil layering impact water flow when different horizons have different hydraulic conductivities (K) or pore size distributions - Water moving from coarse to fine-textured soil will be controlled by properties of the fine-textured soil, leading to a “perched water table” and maybe “throughflow” - Perched water table – an aquifer that occurs above regional water table in vadose zone - Complication: Preferential Flow - Matrix flow – water flow through an ordered soil matrix - Preferential flow – more rapid water flow that follows pathways that bypass the matrix as it infiltrates/percolates (Ex. cracks, root holes, worm holes)
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Major Types: 1) Macropore flow 2) Fingered flow 3) Funnel flow 1) Macropores - Micropores = diameter ≤ 30 µm, relates to textural porosity of soil matrix - Macropores = diameter > 30 µm, relates to structural porosity around soil aggregates - Biological activity – root channels, worms, burrows - Geological forces – subsurface erosion, shrinkage, cracking, fracturing - Man-made – ploughing, drilling wells 2) Fingered Flow – unstable flow resulting from a higher “resistance” to water flow at certain locations in a soil - Caused by horizontal heterogeneity in matrix suction/soil properties, air entrapment or “water repellency” 3) Funnel Flow - Redirection of slow percolation caused by either an obstacle (clay, stone, ice, etc.) or a different texture soil lens (often a coarser texture) - Water in the Saturated Zone (Review diagram) - Aquifer – layer of consolidated or unconsolidated rock that is able to transmit and store enough water for extraction - Aquitard – geological formation that transmits water at significantly slower rate than aquifer - Aquiclude – geological formation that does not transmit water - Confined Aquifer – an aquifer bounded on both top and bottom by aquicludes - Semi-confined Aquifer – an aquifer bounded on one side by a semipermeable aquitard, and an aquiclude on the other side - Unconfined Aquifer – an aquifer without a confining layer above it o Water is recharged to the aquifer along its entire length - Water table – the upper boundary of the saturated zone in an unconfined aquifer - Energy in the Subsurface: Bernoulli - Moving water has 3 interchangeable types of energy (measured in Joules): 1) Kinetic energy – energy of motion 2) Potential energy – energy possessed due to an object’s position above a ref. Level 3) Pressure energy – energy related to pressure - Presuming no loss of mechanical energy due to friction, and presuming water is an incompressible fluid, Bernoulli’s Law: “For steady flow, the sum of the 3 interchangeable types of energy is constant (conservation of energy) mv2 + mgz + pV = constant - Bernoulli and Hydraulic Head - Divide Bernoulli’s Law by volume:
= ρv2 + ρgz + p
- Density and gravitational acceleration are almost constant, divide by ρ and g +z+
= constant
- Neglect the kinetic term because flow velocities so low in ground water, therefore Hydraulic head = Elevation head + Pressure head h = z + - Hydraulic head - Piezometer – tube/pipe with a short screen (opening) at its bottom - Pressure head – means of expressing soil water pressure on a gravitational potential energy basis, per unit weigh of water - Changing soil water pressure to a depth - Equal to the length of water in a piezometer above the screen - Elevation head – the elevation of the screen above an arbitrary datum - Hydraulic head – a measure of the total mechanical energy of the water - Equal to the sum of the Elevation head and Pressure head - Hydraulic Head and Flow Direction (textbook) - Water moves from higher to lower mechanical energy (hydraulic head) - Flow through Porous Media: Darcy (textbook) - Hydraulic gradient – the different in hydraulic head over a porous medium divided by the distance over which the different in hydraulic head is measured - Important the gradient is measured from the water-receiving end minus the waterdispatching end - What did Darcy find? The discharge at steady state was proportional to both hydraulic gradient and the area perpendicular to the water flow! - Darcy’s Law: Q = -Ksat × A × - Porosity vs. Hydraulic Conductivity (They are NOT the same!) - Ex. Sand = lower porosity + higher HC, Clay = higher porosity + lower HC - Homogeneity and Isotropy (textbook) - Homogeneous – K is the same everywhere - Isotropy – K is the same in all directions - Opposites are heterogeneous and anisotropic Lecture 10: Groundwater (continued) and Runoff - Darcy and Ohm (and Fourier and Fick) - Groundwater – movement of water in saturated zone - With Darcy’s Law, you just drop the AREA - Relationship between conductivity (how well something moves) and resistance (resistance to movement) is inversely related (C = ) - Fourier’s Law is some change of temperature over some conductivity of heat - Review Slide 3 (Exercise 3.7.1 in textbook) - Possible Exam Question!
- Recharge/Discharge Systems - Groundwater important to sustaining surface water - Even though there is no rainfall, groundwater maintains flow into rivers because of groundwater recharge - Equipotential lines – lines of equal hydraulic gradient in which groundwater flow lines are perpendicular (90°) to these lines - Streams are “fed” water even without rainfall for a while, known as exfiltration (the discharge of groundwater) - Groundwater Systems and Scale (pg. 101) - There are multiple scales of groundwater flows: - Local - Intermediate (hundreds of meters) - Regional (hundreds of km’s) - Regional and intermediate groundwater are important - Aquifer-Stream Interactions 1) Effluent (gaining) stream – difference between water table and stream surface is called the “seepage face” 2) Influent (losing) stream – surface water providing water to the groundwater 3) Influence stream with “perched stream” – an influent system that is not directly connected to groundwater because it is “perched” above water table 4) Flow-through Stream – simultaneously gains and loses water, mostly water dissolved through rock, and salts also moving into the system - Multiple types of interactions depend on climate and geology - Dissolved ions in water is what makes it conductive of electricity (ex. salt) - How does precipitation become streamflow? - Runoff - Rivers only take up a small portion of a watershed, but they carry the runoff of an entire watershed - Theories of how Rainfall becomes Streamflow (Runoff Generation) - Channel Interception - Hortonian Overland flow - Partial Area Concept - Subsurface Stormflow - Saturated Overland Flow and Return Flow - Macropore Flow - Groundwater Ridging - Variable Source Area Concept * Hydraulic Conductivity is usually a few m/day
- Terms and Definitions - Streamflow – a measurement of water (volume per time) passing a point in a stream - Runoff – the depth of water in a watershed corresponding to the measured streamflow; the process of water movement into streams (depth per time) - Hydrograph – a record of streamflow over time o Any graph with Q and t variables - “Old water” – water that is already stored in a watershed, and also includes the water in rivers - “Event water” – water input into a system during an event (ex. rainfall, snowmelt) - Channel Interception - Actual water falling directly into the channel - Initial rise in hydrograph is often associated with channel interception - Hortonian Overland Flow (HOF) - HOF is a situation where rainfall increases and water cannot infiltrate the ground quickly enough, which results in overland flow - Input rate > infiltration capacity (rainfall intensity exceeding rate of infiltration) - The whole watershed will overflow and entire watershed is streamflow (not just the channel) - Similar idea with a parking lot flooding because infiltration is practically ZERO - Partial Area Concept (PAC) - PAC almost the same as HOF, except it happens on a small portion of the rivers in a watershed (HOF assumes there are vast sheets of water coming into a river) - Subsurface Storm Flow (SSF) - If you have HOF, then you have OLD and EVENT water mixing to produce new water - Most hydrographs are OLD water, not a large portion of NEW water of runoff - Saturation Overland Flow (SOF) and Return Flow - SOF makes a little more sense - Control from above, where water is inputted and water storage is increased where water rises to the surface, the water table intersects the surface so groundwater comes up - Looks like infiltration flow, but stick a well into the ground and the water will come up - Ground Water Ridging (GWR) - GWR is one way to make SOF come up (for the watertable to come up) - Capillary fringe is relatively saturated and close to being a water table, and only a relatively small amount of water is needed to cause a rise in water - Groundwater tables tend to be near the surface near water zones - Macropores and Quick Subsurface Flow - Animal burrows - Dead tree and plant roots - Worms - These tunnels are visible but hard to quantify or study
- Variable Source Area Concept - Similar to SOF where areas near sources of water tend to get wetter, and after rainfall you get some more saturated areas, and over time these saturated areas expand - Majority of shaded areas (on the diagram) are areas that intercepts rainfall and give quick means for water to be input into the river system Lecture 11: Runoff and Streamflow - Importance of Understanding Streamflow dynamics - Water Supply – the huge supply such as lakes which are mostly fed by rivers - Important to understand the inflows and outflows to track the supply - Water Quality – the constituents within water in a stream are controlled by the pathway water takes to get to a stream - Flood Prediction – understanding past streamflow records allow us to make educated choices about certain actions Ex. determining the necessary height of a dam, warning of potential future floods - Factors affecting runoff 1) Watershed size – the bigger the more water in it, and streamflow generally decreases downstream 2) Topography – how hilly or how flat, affects how water gets into a stream - Runoff always occur downhill, perpendicular to contour lines 3) Shape – flow from various parts of watershed are affected by the shape of the watershed, such as long-narrow or circular 4) Aspect/Orientation – which way it is pointing is important for energy, orientation, latitude, slope, etc. 5) Geology – affects soil formation, thickness, slope/gradients, drainage, made watershed boundaries 6) Soil – soil properties can affect hydraulic parameters - Measuring Streamflow – it is done physically or mathematically - Discharge = velocity × cross-sectional area Q = vA (because L/T × L2 = L3/T = m3/s) - Velocity-Area Method - Measuring Velocity 1) Using a tool while in the water to measure how fast (velocity) water is pulling you 2) Using a windvane-like device and measure how many clicks over a time period 3) Yellow tail spins to measure revolution to get downfall velocity - 6/10 depth vs. 2/10 and 8/10 depth methods - Depending on the depth of the stream - When stream depths < 0.75 m, average velocity assumed to be about 6/10 depth below surface of water (4/10 above bottom) - In deeper streams, average measurements made at 2/10 and 8/10 depths
- Velocity-Area Method - You take the stream and break it into specific sections that are more easier to measure because velocities will be different - Representative velocity is some point in the middle of each line, add them all up to get your total velocity of discharge (middle of those two dashes on each line) - The Rating Curve - The Gaging Station - Basically it is a big well with instruments that record water levels, and as water levels go up, the well will go up as well - Dilution Gauging - A chemical method that adds a tracer in water (such as salt, dye that creates colour) - Concept is to add the tracer at some location at a known rate, and at a certain distance, that tracer will mix itself with water, and at some point the river will be well-mixed - More accurate than area-velocity QCu + QiCi = (Q + Qi)Cd Q = Qi - Weirs and Flumes – restricts cross-sectional area of streams - Weir – restricts depth to flow over a notch that is raised above the stream bed - Generally like a dam, where water flows over a v-notch - Flume – restricts both depth and width - More expensive to install, but self-maintaining - Flow Over a Weir (No need for a rating curve) Q = 1.18 × CdB × h1.5 - The Hydrograph (refer to textbook page 244) - Tells alot by its shape as to what is going on - Relatively a discharge over time, starts to go up with flow - Antecedent flow rate – before rainfall - Time of rise – the different of time lag, basin lag - Peak flow - Falling limb - Hydrograph separation line - Groundwater recession - Hydrological Regimes - Hydrological Regime – the entire state of water movement in a watershed - Runoff regime – the characteristic response of runoff in a watershed given its climate and geography - Important Runoff Regimes in Canada - Nival Regime – snowmelt dominated (Canada mostly covered by this) - Occurs around march or april when snowmelt occurs - Pluvial Regime – rainfall dominated - Glacial Regime – glacier-melt dominated
- Similar to nival regime, you get peakflow around spring - But the difference is that the peak is shifted intot he summer because these areas warm up later (delayed because of their geography) - However, peakflows remain similar to nival regimes, just shifted Lecture 12: Flood Analysis and Water Quality - Hydrograph Separation - The point is to distinguish “baseflow” from “stormflow” (arbitrary) a) Constant discharge method b) Constant slope inflection point method c) Concave curve inflection point method - Runoff Ratio of Coefficient (RC) - Measures the amount of precipitation input that is observed as discharge -
RC =
- What is a Flood? - An enormous flow down the river - Many ways to get a flood, such as a huge tide, a big bay can move large amounts of water can also flood - Floodplains – areas known to flood often 9and homes are built on them) - Flow Duration Curves - Constructing a Flow-Duration Curve (IMPORTANT, need to know how to read it!) - Weibull Formula (review example on slide 9) - Calculates return periods (T) or probabilities of exceedence (P) -
T=
P=
- Flood Probability Short Cuts - Probability that an RP-return period flood will be exceeded in ALL of next n years = [ 1 RP]n - Probability that an RP-year return period storm will be exceeded at least once in n years = 1 – [ 1 – 1/RP ]n - Probability that the next time an RP-return period flood will be exceeded is n intervals from now = [ 1 – 1/RP ]n-1 × 1/RP - Limitations of Frequency Analysis - Review slides 15 to end
=
(assuming input = output)
- Spatial distribution of Water - The Hydrological Cycle 1) The land receives more precipitation than evapotranspiration 2) Oceans evaporate more than it receives precipitation 3) Excess of water on land returns to oceans as runoff, which balances #1 and #2 - Principle driving forces of the Hydrological cycle: Solar energy and gravity - Spatial variability in global precipitation (the “middle finger” graph) - Spatial variability in global evapotranspiration - Spatial variability in global run off - High precipitation + low evapotranspiration = high runoff - Low precipitation + high evapotranspiration = low runoff - Hydrological Models - Empirical – statistical relationships, not robust - Deterministic – known physical relationships, more robust - Stochastic - statistics - Typical Hydrological Model Structure - Basic models: inputs model outputs - Complex models: outputs may be used for inputs for another model - Typical inputs and outputs - Sensitivity Analysis - Small change = not sensitive, big change = sensitive - Models are made for relative comparisons, and variables with no sensitivity are insignificant in the model - Physicochemical Properties of Water - Molecular structure of water - 3 States: solid, liquid, gas - Hydrogen bonding, strong covalent bonds between O and H - Without H-bonding, water would be a gas (water vapour) at room temperature - Asymmetric structure - 105° angle between the 2H’s in H-O-H - Surface tension, an electrochemical attraction because of hydrogen bonding
- Capillarity – the upward movement of water, due to effects of wetting and surface tension - Meniscus - The smaller the diameter, the further water can travel up a tube - Phases of Water (remember the terms and molecular structure) - Liquid (Water) and Solid (Ice) – freezing and melting - Liquid (Water) and Gas (Water vapour) – vaporization/evaporation and condensation - Gas (Water vapour) and Solid (Ice) – sublimation and sublimation - Sublimation – solid turning into gas (and vice versa) without becoming a liquid - Why do ice cubes float? - Water density maximum is 1.00g/cm3 at 4°C - When temperature drops below that, water becomes less dense and forms hexagonal crystals of ice (less dense), therefore ice floats - Density of Water - Water contracts as it cools, but only to a point at 4°C - Beyond 4°C, water expands as more H-bonds form hexagonal structures until -29°C - Phase Changes - Heat energy is either absorbed or released to change from one phase to another - Amount of heat energy required to break the h-bonds - 1 calorie = 4.184 J (joules) - Ice Water Water Vapour – latent heat is absorbed to break h-bonds - Water Vapour Water Ice – latent heat is released to form h-bonds - Latent Heat (2 types) - Latent heat – involved in phase changes of water - Sensible heat – heat that you “feel” or “sense” Lecture 3: The Energy Balance and Water in the Atmosphere - Radiation – energy in the form of waves and sub-atomic particles - Planck’s Law – wavelength of energy emitted by a surface decreases as temp increases - Wien’s displacement law – calculates wavelength at which max energy radiation occurs - λmax =
T = temperature (in Kelvin)
- The electromagnetic spectrum - Shorter λ = blues, violets - Longer λ = reds - Energy pathways and principles - Driver of energy on Earth is radiation from the Sun - Drivers of spatial & temporal variation: seasons, latitude, clouds, surface characteristics - 1 µm = 1.0 × 10-6 m - Insolation = INcoming SOLar radiATION - It is shortwave radiation (inputs are UV, visible light, near-infrared wavelengths) - Energy outputs from Earth
- Surface Radiation Balance - Direct vs. Diffuse radiation - Shortwave vs. Longwave radiation - Water vapour the most dominant GHG, absorbs Earth’s long λ - GHG increase absorption of energy, not necessarily more reflectivity - Measuring energy depends mostly on the surface temp of the body emitting it - Wien’s law = what type of energy - Stefan-Boltzmann law = how much energy moved per area per unit time - QR = ƐσT4 - Blackbodies – 100% efficient in emitting energy (Ex. Sun, Earth) - Darker things tend to have higher Ɛ, lighter things have a lower Ɛ - Solar constant - Sun’s energy arrives at edge of atmosphere at an average of 1.74 × 1017 W - Area of Earth is 1.28 × 1014 m2 - Isc = Sun’s Energy / Area of Earth = 1367 W m-2 Solar Constant - Energy Balance (Fig. 3.2 slide 17) - About ½ of the energy received at the top of the atmosphere is absorbed by the Earth - Clouds and atmosphere play a role in absorption and reflection - Outgoing energy + Incoming energy = 100 (100 units represents the solar constant) - Albedo – determines the ability of a substance to reflect energy - Albedo = reflecting radiation / incoming radiation α = ↑K/↓K - Albedo of water extremely variable because of surface, angle of incoming radiation, etc. - Smooth surfaces increase α while rough surfaces decrease α - Incoming radiation (energy) is absorbed, moved around (spent) as sensible energy - Radiation balance (Q*) - Short λ energy balance = incoming short λ – reflective short λ K* = K↓ - K↑ - Reflective short λ = albedo × incoming short λ K↑ = αK↓ - Long λ energy balance = incoming long λ – reflective long λ L* = L↓ - L↑ - Radiation balance Q* = K* + L* (net radiation) - 24 hour Q* graph - Heat Transfer at Earth’s surface by several processes - Conduction – molecular transfer - Convection – heat transfer by vertical movement - Advection – heat movement of liquid or gas horizontally - Expenditure of Net Radiation (Q*) - 3 ways that net radiation is expended from a surface: LE, H, G - Latent heat of Evaporation (LE) – energy stored in water vapour as water evaporates - Sensible Heat (H) – back and forth transfer between air and surface via convection and conduction - Ground heating or cooling (G) – energy flowing through ground only via conduction
- Relationship between Net Radiation (Q*) and Expenditure of Net Radiation - We already know that Q* = K* + L* - Expenditure Q* = ∆LE + ∆H + ∆G - So therefore, K* + L* = ∆LE + ∆H + ∆G - Partitioning of LE and H - Main factor is available moisture - A system that is moist will use more latent energy - A system that is dry uses more sensible energy (less water to evaporate) - Review the example of you being at the shore vs. in the middle of the lake! - Bowen Ratio – describes type of heat transfer in a water body -
-β=
β > 1 = more H than LE, β < 1 = more LE than H
- Importance of Precipitation - Latent energy a driving force for evaporation and precipitation - Rain and snow are main hydrological inputs to the surface of the Earth - Precipitation a major control on vegetation and ecology - Understanding precipitation inputs is critical (ex. Planning purposes) Lecture 4: Precipitation and Interception - Forming Precipitation (3 processes must occur) 1) Cooling to the dew point 2) Condensation onto nuclei 3) Droplet growth - For precipitation to occur for any appreciable time, this 4th process must occur 4) Importation of water vapour (ex. hurricanes suck in so much air which leads to more precipitation) - Cooling to the Dew Point - Dew point – the temperature at which a given parcel of air becomes saturated - Condensation occurs when air parcel cooled beyond dew point or if moisture is added to an air parcel already at dew point - Vertical uplift the common means of cooling air, results in adiabatic cooling - Adiabatic Cooling - The cooling of an ascending air parcel without heat exchange between the parcel and surrounding air mass - Air parcel expanding as it rises because less pressure - Review the 4 key points of air parcel and adiabatic cooling (slide 31) - Dry (DALR) vs. Saturated (SALR) Adiabatic Cooling - DALR: 1°C / 100 m (when parcel of air < saturated vapour pressure) - SALR: 0.5°C / 100 m (when parcel of air ≥ saturated vapour pressure) - Review the Saturation Vapour Pressure graph - Saturation Vapour Pressure – the pressure exerted by water vapour molecules in the air when air is saturated with water vapour
- Lifting Mechanisms - Adiabatic cooling of air parcels require “uplift” - Mechanisms of uplift: - Convectional lifting – air rises by local surface heating, short intense storms - As warm air rises, other air takes its place - Orographic lifting (topography) – topographic barrier force air to rise, chinooks - Frontal lifting (convergence) – contrasting air masses converge with warm air rising over cold - Cold front – cold air mass moving into warm air mass, short violent precipitation Ex. large raindrops, heavy showers, lighting, thunder, hail - Warm front – warm air mass moving into cold air mass, longer duration drizzly shower - Condensation - Need cloud condensation nuclei (CCN), particle impurities in atmosphere > 10-4 mm - When dew point is reached, CCN provides surfaces on which water can condense - “Cloud seeding” (silver iodide) - Droplet Growth - Droplets in cloud (0.001-0.02 mm) must grow to about 0.4 – 4 mm - This happens through drop collision, coalescence or ice-crystal growth - 2 reasons for droplets not reaching the ground: Evaporation or Friction - Warm clouds (temp > 0°C) - Collision-coalescence process – turbulent mixing of droplets cause collision and growth - Creates light drizzle, primary mechanism in tropical regions - Cold clouds (temp < 0°C) - Super-cooled water – liquid water chilled below freezing point without becoming solid - Bergeron-Findeisen Process - Importation of Water Vapour - Concentration of liquid water in most clouds only 0.1 – 1 g m-3 - Not enough water in most clouds to produce significant rain, water vapour needs to be continually added into clouds - Winds converging provide a source of moisture - Important Precipitation Parameters - Type – rain, snow, hail, sleet, etc. - Depth – expressed in mm - Duration – how long - Intensity – rate of precipitation over a period of time (mm/hr) - Return Period – likelihood a given precipitation even will occur - Influences on Precipitation Distribution - Static influences – altitude, aspect, slope - Dynamic influences – source of water, variations in surface water temp, convectional uplift mechanisms
- Impact of Altitude – Rainshadow effect - Chinook winds – warm dry downward sloping air caused by adiabatic warming - These warm winds lose its moisture on the downward slopes, can make snowmelt - Minor impact of slope and aspect on measuring precipitation - Interception – interception of precipitation by vegetation or buildings - 10-40% (average) of gross precipitation is lost to interception loss - Interception loss – precipitation intercepted by vegetation that evaporates back into atmosphere - Interception Processes - Gross rainfall (R) – rainfall measured above vegetation or in the open R = Rt + Rs - Interception (I) – storage of precipitation on surfaces where it is subject to evaporation - Throughfall (Rt) – rainfall that reaches the ground passing through canopy - Stemflow (Rs) – water that reaches the ground from running down trunks or stems - Canopy Interception Loss (Ec) – water that evaporates from canopy - Litter Interception Loss (El) – water that evaporates from ground surface (litter, leaves) - Total Interception Loss (Ei) = Canopy loss + litter interception loss Ei = Ec + El - Net Rainfall (Rn) = Gross rainfall – Total Interception loss Rn = R – Ei = (Rt + Rs) – (Ec + El) - Net vs. Gross precipitation - Net precipitation – what actually gets to the ground - Gross precipitation – the total precipitation - Leaf Area Index (LAI) – the ratio of leaf area to ground surface area - LAI > 1, more than 1 layer of leaf per ground area, more likely to intercept (but throughfall can also occur indirectly if canopy storage capacity is exceeded) - LAI < 1, there are openings in the canopy to allow direct throughfall - Funneling effect of Interception - Deciduous trees grow like a “funnel” and have substantial infiltration of water into the ground at the stem and outside of canopy cover - Stemflow in most systems often less than throughfall - Stemflow - Often not well measured - Best measurement procedure is to directly measure all trees within a plot 1.5x the diameter of the largest tree’s crown in the plot - Create an eavestrough, wrap around bark at least once, collect water in can to be weighed - Coniferous vs. Deciduous tree interception - Coniferous intercept 10-15% more than Deciduous on an annual basis - Deciduous trees lose their leaves, but during growing season they are equal - Also depends on the season, coniferous trees can hold snow (makes a big difference) - Canopy structure makes a big difference, pine (needles) vs. fir-hemlock (dense leafing)
- Factors affecting Interception - Vegetation type, time of year, and size affect interception - Measure Leaf Area Index (LAI) to explain these effects - How precipitation falls (intensity, duration, frequency, etc.) is a major control o Intensity: more intense = less interception o Duration: longer = less interception o More frequent = less interception - Wind affects evaporation and interception, snow is easily intercepted but can be blown off by wind as well - Measuring rainfall depth - Rainfall depth – the real depth of a layer of water on a flat impermeable surface after rainfall - Recording rain gauge – device that measures rainfall intensity - Rainfall intensity – rainfall measured in a short period of time (mm/hr) - Precipitation Gauge types - Weighing raingauge - Float and Siphon - Tipping bucket - Measurement Accuracy – many factors affect precipitation measurement accuracy - Orifice (opening) size - Orifice orientation – flat, facing a slope, horizontal rainfall - Orifice height (from surface) and shielding – the higher the more windspeed - Nearby obstructions – must be well-exposed, avoid rainshadows - Splash, evaporation, wetting losses, snow blown off by wind - Good practices to prevent problems of measurement inaccuracy (Pg. 30) - Shielding reduces turbulence - Setting up apparatus, you want the distance of the raingauge from obstructions to be 2x the height of obstructions - Areal Estimation of precipitation – point measurements in a region as area estimates of precipitation for an entire region (such as watersheds) - Arithmetic average - Thiessen polygons - Hypsometric method - Isohyetal method – good for cases when majority of rainfall takes up a watershed Lecture 5: Rain and Snow - Review sample exam questions at beginning of lecture slides - The Importance of Snow - It stores water over several months and then releases it quickly (on average 150 mm) - Snow and glacier melt a major source of fresh drinking water
- How does snow fall? - Instead of condensation, water vapour undergoes sublimation - Sublimation – rising air (100% saturated) reaches its frost point (temp ≤ 0°C), and the water vapour in that air parcel changes to ice without passing through liquid state - Snow falling is crystalline, and snow accumulating on ground becomes granular - Warm clouds – rain comes down as rain (never snow!) - Cold clouds – snow remains cold and falls as snow (when heavy enough), and it remains as snow if it hits a cold ground - Snow Hydrology terms - Snowfall – depth of solid precipitation on surface over a time period - Snowpack – accumulated snow on the ground at time of measurement - Snow water equivalent (storage term) – total volume of liquid water that would result from melting a snowpack over a given area (ex. depth) - Snowmelt – depth of liquid water produced by melting that leaves the snow pack over a time period - Ablation – total loss of water (depth) from a snowpack over time Ablation = snowmelt + evaporation/sublimation - Water output – depth of liquid water (including rain on snow) leaving a snowpack over a time period - Porosity (Ф) – volume of air and water over the total volume of the snowpack Ф= -
Liquid-water content (ʘ) – the ratio of water to total volume ʘ=
- Snow water equivalent Height of melted water =
× height of snow hm =
hs
- Snowpack changes over time - Freshly fallen snow has a density ratio (ρs/ρw) between 0.004 to 0.34 Once deposited, 4 metamorphism mechanisms make it more dense until melt is complete: 1) Gravitational settling – settling increases due to weight of overlying snow, and temperature of that layer 2) Destructive metamorphism – snowflakes evaporate and vapour deposits on surfaces creating larger, spherical snow grains - As melting occurs, snowflakes become more dense and have less air space in between 3) Constructive metamorphism – most important pre-melt densification process in seasonal snow (Review slide 19) - Sintering – two snow grains touch build a “neck” between adjacent grains as some melted waters re-freeze - Sublimation can occur in warmer sections, and vapour moves toward cooler spots where condensation occurs
- Depth hoar – snow near base sublimates at a high rate, leads to basal layer of large planar crystals low in density and strength 4) Melt metamorphism 1) Liquid water at surface freezes in cold snowpack, making it more dense (layers of solid ice) 2) With the presence of liquid water, smaller snow grains disappear and larger ones (sand size) dominate - As snow melts over time, these 4 mechanisms may occur until the snow fully melts - How does Snow Melt? - Melt starts to occur when net input of energy into the snowpack turns from – to + - 3 Important stages of snowmelt (important for exam!) 1) Warming phase 2) Ripening phase 3) Output phase – you only see water come out at this phase! 1) Warming Phase: - The phase when snowpack temperature increases steadily until it is “isothermal” at 0°C - Cold content (Qcc) – the amount of energy required to raise the average temperature of a snowpack to the melting point (0°C) - Qcc = -ci × ρw × hm × (Ts – Tm) 2) Ripening Phase: - The phase where melting occurs and the build up of liquid water up to the point (max) where it leaves (the output phase) - At the end of this phase, snowpack is “ripe” because isothermal at 0°C, cannot retain any more liquid water - Liquid water retaining capacity: hwret = Ɵret × hs - Total energy required to complete ripening phase: Qm2 = hwret × ρw × λf = Ɵret × hs × ρw × λf 3) Output Phase: - The phase when more energy inputs into the snowpack result in water leaving the snowpack - Total energy required to complete output phase (Qm3) = amount of energy needed to melt snow remaining at the end of the ripening phase Qm3 = (hm – hwret) × ρw × λf this equation is missing time - Estimating Snow Loss by Melting Measure water output: -∆hm =
= ∆w
- Alternative Method for Estimating Melt Water: Degree Days - An EMPIRICAL method, best used during overcast periods - M = K (Ta – Tb) - Measuring Snowfall using gauges: Nipher Snow Gauge - Used to capture snow and measure its water content in mm - It is mounted on a sliding metal pipe, so when snow accumulates, it can be raised to keep top edge 5ft above the surface of the snow (prevents ground snow from drifting in)
- The Easy way to measure snow (Manually) - Measuring the snowpack: Stakes: - Stakes driven into the ground surface before winter, and monitored at regular intervals - Density usually assumed Survey: Use a snowcore, stick it into the snow to find depth and to measure volume Use of fish scales to measure weight hm = hs Snow Pillows: - A device used for measuring snowpack, made of glycol or fluid-filled rubber pillow that will not freeze - It measures the water equivalent of the snowpack based on hydrostatic pressure created by overlying snow - Its large size (1 – 4m diameter) minimizes any discrepancy due to bridging of snowpacks Lysimeters: - A measuring device which can be used to measure the amount of actual evapotranspiration (which is released by plants, usually crops or trees) - It records amount of precipitation that an area receives and the amount lost through the soil, which allows you to calculate amount of water lost to evapotranspiration Lecture 6: Evapotranspiration - What is Evapotranspiration? - The sum of evaporation (oceans + land) and plant transpiration from the earth’s surface to the atmosphere - ET controls water vapour in the atmosphere, which controls climate and how to understand climate change - ET the 2nd most important flux, precipitation is 1st, forms balance in hydrological cycle - Evapotranspiration – the net loss of water through the sum of evaporation and transpiration - Evaporation – net loss of water from a surface due to change in liquid to vapour, and net transfer of the vapour to the atmosphere - Transpiration – net loss of water from within the leaves of plants through stomata - You need energy to change the phase, and some sort of force to move the vapour away - Evapotranspiration in the Hydrological Cycle - 62% of Precipitation on land is lost to ET, 112% of precipitation on oceans is lost to ET - Factors required for Evaporation 1) Available energy 2) Available moisture (Ex. In the desert there is little to no evaporation) 3) Capacity for water vapour in the atmosphere (if no capacity then no movement)
1) Available Energy - Main source of energy for ET is from the Sun - It is the net accumulation of energy at the surface (Q*) Q* = QS ± QLE ± QG - When water moves from liquid to gas, energy is absorbed, so QLE is a negative flux Lesser forms of Available Energy 1) Anthropogenic Energy – things like heating of houses or heat produced by vehicles 2) Advective Energy – horizontal flux of energy (often latent energy) blown from far away 2) Available Moisture - “Open” water (ex. lakes, ponds) evaporate more freely, denoted by Eo - Soil surfaces have smaller supply of available moisture, and as surfaces dry out, it becomes more difficult to “pull” water up against forces of gravity and tension Lecture 7: Evapotranspiration (Continued) and Soil Water - AET vs. PET - PET (Potential Evapotranspiration) – the amount of ET that would occur if water were NOT limiting (Ex. lakes) - AET (Actual Evapotranspiration) – the actual amount of ET that occurs whether water is limiting or not - Lakes evaporate at a potential rate, soils do not evapotranspirate at a general rate - AET difficult to measure, PET generally used for measurements (but need caution!) - The Receiving Atmosphere and Gradients - Like many physical processes in the environment, ET driven by gradients - Fick’s First Law of Diffusion relates diffusive flux to the concentration, postulating that the flux goes from regions of high concentration to low concentration -
Jj = -Dj
- Water in the Atmosphere: Vapour Pressure - Evaporation affects and is affected by amount of water vapour in atmosphere near the evaporating surface - Vapour Pressure (e) – the “partial pressure” of water vapour - Saturation Vapour Pressure (e*) – the max vapour pressure that is thermodynamically stable (function of temperature) - Vapour Pressure Deficit = e* - e (there needs to be a deficit for any movement) - Saturation Deficit of Overlying Air Controls Vapour movement - Evaporation is proportional to es* - ea (vapour pressure deficit) - Equilibrium would be reached quickly and evaporation would stop if not for wind - Therefore, 2 main controls on the rate of evaporation from an open-water surface: 1) Windspeed (controls air turnover) 2) Vapour Saturation Deficit (controls uptake) - Humidity - It is a term for water vapour in the air, not “moist” air - It is measured in different units, and measured using a psychrometer
Absolute Humidity – the actual amount of vapour in the atmosphere (this really IS vapour pressure) - Relative Humidity – the percentage saturation of an air parcel at a specific temperature RH = e/e* × 100 (%) - How a psychrometer works (Review slide 21) - Vegetation Canopy ET - Evapotranspiration at top of vegetation canopy is a mix of: 1) Evaporation from soil 2) Transpiration from leaves 3) Interception loss - Transpiration - Water leaves stoma because of vapour pressure gradient results in a “pull” from the roots out the leaf - Mechanisms to reduce transpiration: leaf wilting/curling (reduces leaf area), alteration of orientation to sun energy, closure of stomata (caused by plant wilting) - Interception Loss - Biggest influences 1) Canopy structure 2) Meteorology (atmospheric conditions) - Canopy Structure 1) Storage capacity 2) Drainage characteristics (ex. Rhubarb) 3) Aerodynamic roughness (turbulence induction) - Meteorology 1) Rainfall characteristics (intensity, duration, frequency) - Measuring PET and AET - PET measured by pan evaporation, ET gauge - AET very difficult to measure - Direct Micro-Meteorological Methods - These methods attempt to directly measure how much water is evaporated above a surface - 3 main methods: 1) Eddy correlation 2) Aerodynamic profiling 3) Bowen ratio - Spatial scales are generally small - Mostly used for calibration of estimation methods 1) Eddy Correlation – measures and calculates vertical turbulent fluxes within atmospheric boundary layers -
-
E=
× ua’ × q’
2) Aerodynamic Profiling – calculates the energy available for evaporation - Require vertical humidity gradients (humidity and temperature) - Assumes atmosphere is neutral and stable (not always the case) 3) Bowen Ratio – Measuring H (sensible heat) and LE (latent heat energy) is difficult, but it is relatively easy to estimate the H/LE (Bowen ratio β) - More relaxed atmospheric assumptions -
β=
=
E=
- Water Balance Approaches - Try to solve for ET in the water balance - Often, everything BUT evapotranspiration is measured, so there may be many errors - Principle approaches: 1) Evaporation pan 2) Lysimeters 3) Soil water depletion over time 4) Watershed water balance 1) Evaporation Pan Approach: E = ceEp (Ep = ∆S – P) 2) Lysimeters – use an isolated plot that is under the same conditions as surrounding area - Conduct a water balance dominated purely by irrigation and ET - Best way to measure ET, but very expensive (worth 4 houses) - Often used to make a pan coefficient 3) Soil Water depletion over time - Need to monitor VMC of soils between periods of time under relatively strict conditions: - Water table considerably deeper than root zone - Easiest when runoff and drainage are ZERO 4) Water balance approach AET = P = Q ± ∆G ± Ɵ, and over a long period potentially: AET = P - Q - Generally used at large scale (watershed) - Errors with certainty of these variables can be up to 50-100% - Empirical/Theoretical Estimation - These techniques use climatological variables known to influence ET and uses them to stimulate ET most estimate PET (potential evapotranspiration) - 2 Popular Approaches: 1) Thornthwaite Method 2) Penman and modified approaches (more approaches AET) - Thornthwaite Method - This method is for monthly ET only, and highly EMPIRICAL - Calibrated for humid temperate regions - Need only mean monthly temperature (T) and latitude
-
]a
Etp = 16b [
- This takes into consideration the energy available of evapotranspiration of water - Thornthwaite Heat Index I=
1.514
a = 6.7 × 10-7I3 – 7.7 × 10-5I2 + 0.018I + 0.49
-
This is empirical and not accurate because “a” is “fudged”
-
To calculate “b” b =
×
(24)
- Penman-Monteith Equation (Slide 16) - Deterministic, physically-based model for evaporation that includes both the energy required to evaporate water and the atmosphere’s ability to receive vapour - Takes into consideration biotic control (resistance) Ea =
×
Simplified: Ea = 0.408 ×
∆=
- Aerodynamic Resistance (ra) - It is the resistance (inverse of conductivity) encountered by water vapour in diffusing into air from a surface (vegetative or open water) - It is reciprocal to the roughness of the earth’s surface and wind speed near surface Ex. Rougher surface + stronger surface winds = more turbulent mixing + less resistance to evaporation - “Unstressed conditions” (AET = PET), ra decreases with roughness - Surface Resistance (rs) - It is a physiological resistance imposed by vegetation stomata on the movement of water vapour by transpiration - It is variable in relation to moisture availability (Ex. Open water = 0 s m-1 b/c no limit) - “Unstressed conditions” then Penman-Monteith solves for PET - Surface resistance opposite to Aerodynamic resistance: high rs low ra, low rs high ra - The difficulty of Modeling - ET calculated by Penman-Monteith is sensitive to resistivity terms, which are difficult to accurately parameterize - Often Penman-Monteith only useable in research situations - Estimations often applied through Reference Crop Evaporation approach - Reference Crop ET – based on ET from an “idealized” surface - A grass crop with uniform height and specific features: 12 cm high, albedo of 0.23, and surface resistance of 69 s m-1
- Reference Crop Evaporation - Reference crop evaporation (given ra and rs) are multiplied by a “crop coefficient” (Kc) for a particular crop to arrive at PET - Kc changes with different growth stages of a crop, it is not a constant - Ra calculated for the reference crop as 208/u2, where u2 is wind speed at 2m height Ep = Kc × Erc - Where is water “stored”? - Water hits the ground and infiltrates into the soil water (unsaturated) and groundwater (saturated) - Soil is not really a barrier, it has particles and air spaces - The smaller these air spaces (pores) the more capillary action - A zone that has all its spaces taken up by water is “fully saturated” - The water table is the boundary between soil water and groundwater - Soil is Beneath us, What is it? - They contain pore spaces with different structures, porosity, and permeability - Sand – macropores, many large spaces (lower porosity, higher permeability) - Clay – micropores, many small spaces (higher porosity, lower permeability) - Soil descriptors: Particle size - Clay = 0.0002-0.002 mm, Silt = 0.002-0.02 mm, and Sand = 0.02-2.0 mm - Soil descriptors: Texture - Many different mixtures of the above 3 give you different porosity and permeability Ex. Loamy Sand, Clay Loam, etc. - Soil Matrix: Air, Water, Soil - Total volume = volumeair + volumewater + volumesoil Vt = Va + Vw + Vs - Vv = Va + Vw -
Porosity = (volumeair + volumewater)/total volume
=1-
=n
- Volumetric Soil Moisture -
Volumetric Moisture Content (water content) Ɵ =
Ɵv =
- This will always be equal or less than porosity - 1000 cm3 = 1 kg - Characteristics related to Soil Mass - Total mass of soil mt = ma + mw + mt - Gravimetric soil water content Ɵg = -
Bulk Density =
ρb =
- Infiltration of Rain and Melt Water into the Ground - Infiltration – the passage of water through the surface of the soil, via pores and small openings, and into the soil profile - Fundamental interface process between atmosphere and lithosphere
-
Highly dependent on soil characteristics, sustains plant growth, recharge groundwater, decreases runoff and erosion, retards (slowing) pollutant transfer to surface water - Infiltration - 2 Principles affect downward movement of water in soil profile (percolation) 1) Tension forces (suction, matric, capillary), directly related to h-bonding between water and walls of soil pores 2) Gravitational Forces - Infiltration terms: - Infiltration rate – rate of water entering soil (mm/h) - Water input rate – rate at which water arrives at the surface (ex. rainfall intensity) - Infiltration capacity – max rate at which infiltration can occur for a certain condition - Depth of ponding – depth of water standing on surface - Factors that affect infiltration – review Slide 35 Lecture 8: Soil Water Zone, Infiltration, and Percolation - Pressure/Tension in the Soil Water (Unsaturated) Zone (also called Vadose Zone) - Pores spaces in an “unsaturated” zone have a NEGATIVE pressure (meaning less than atmosphere pressure) - Negative pressure is “matric potential” or “matric suction” - Matric potential has a negative sign, but matric suction is the absolute value of matric potential - Soil Water Tension - Adhesion – attraction of water to sides of a pore - Cohesion – attraction of water to water - The smaller the radius of the pore, the larger the potential (more suction) - Moisture and Tension - Suction in smaller pores > larger pores - Suction in drier pores > wetter pores - When dry soil is wetted, smaller pores fill first, drainage is first from larger pores - Physical Measurement of Tension - Tensiometer – an instrument used to determine matric water potential (Ψm) (soil moisture tension) in the vadose zone (unsaturated zone) - Soil Moisture Characteristic Curve - Pore size distribution differs between soils - Relation between volumetric soil moisture (Ɵ) and suction (-Ψ) also differ between soils - When you’re wetter, matric suction goes down - Relationship is NOT linear, not as simple as y = mx + b - Sand is well-sorted, suction initially “drops off” (like a “jump”) and then levels off - Clays have significantly higher suction, and also higher volumetric moisture content - Clay is very porous, so VMC is high, but water does not move very well
- Soil Water Classification - Hydroscopic water – water permanently attached to outer edge of a piece of soil o Impossible to get off unless dried or evaporated o This water is not available to plants, plants do not have enough suction power - Capillary Water – water held by adhesion/cohesion o Important for plants, plants have slightly higher power to obtain capillary water - Gravitational Water – excess of capillary water o Any water excess of Field Capacity is excess gravitational water - Field Capacity – max VMC (Ɵ) that a soil can hold against gravity - Wilting point – VMC (Ɵ) at which plants can no longer extract water from soil - This is no longer gravitational water; it is water that plants can no longer obtain - Clay = high FC and WP - Sand = low FC and WP - The area with the most available water is between FC and WP, tend to be loamy soils - “Available” Water - Typical soil has FC at pF = 2.0, and WP at pF = 4.2 (pF = log (suction –Ψ)) - Therefore, available soil water for plants is between pF = 2.0 and pF = 4.2 - Water held between pF = 0 and pF = 2.0 will drain (VMC 30-40%) - Water between 0-10% VMC will not move - Saturation occurs at pF = 0, which is around 42% porosity - Seasonal Changes in Soil Water Storage - Spring, lots of snowmelt and excess water above FC - Summer, plants suck water and transpire alot of water, so percolation water is drained, more sucking and transpiring than water coming in - Fall, loss of leaves and plants die, transpiration decreases and less sucking of water, therefore water content begins to increase again - Summer = deficit, Fall = recovery - Drying and Wetting: Hysteresis (Study the graph for the EXAM!) - What is going on between Drying curve and Wetting curve? - Soils are not drying as much in relation to wetting at higher VMC because dry soils stay wetter at that stage, large pores drain first while smaller pores drain last - Hysteresis – “Ink Bottle” Effect and Contact Angle - Water content stay higher longer when draining in hysteresis - “Bottle neck” holds water by hydrogen-bonding which results in higher water content on draining over time - Meniscus appears because of h-bonding on sides, but gravity pushing it down - Flow in the Unsaturated Zone - 2 Things determine how much water goes through at a time 1) Gradient Pressure – water always move from high pressure to low pressure
-
2) Saturated Hydraulic Conductivity – max rate at which water can physically move through soil Water is more easily moveable in wetter soils than drier soils
-
Darcy’s Law: q = -K(Ψ)
Q = -kA
- Upward Flow: Capillary Rise - Capillary Rise – the sucking up of water from below through capillary forces - Leads to “Capillary Fringe” – the subsurface layer above a water table in which groundwater seeps up by capillary action to fill pores - Its height limited by air-entry suction of the largest prevailing pore size above water table - Downward Flow: Infiltration & Percolation - Infiltration – passage of water through the surface of the soil, via pores or small openings, into the soil profile - The initial time that water goes through the surface, how quickly depends on suction - Percolation – the downward movement of infiltrated water - Dry soils initially pull the water, then gravitational forces moves it downward - Infiltration – review slides, this was mentioned in previous lecture - 2 Principle factors affect percolation: tension forces, and gravitational forces - Physical Measurement of Infiltration - One easy way is to input water as water is draining out to maintain a balance, then measure the input water rate - Numerical Estimation of Ponded Infiltration: Green Ampt Equation (Skip!) Lecture 9: Soil Water (Continued) and Groundwater - Zero Flux Planes - After rainfall, infiltration continues, but at the same time water above it also evaporating - These two processes meet in the soil profile and creates a “no flow” situation, also known as a “Zero Flux Plane” or “Divergent Zero Flux Plane” - Typical in spring through summer - Autumn, P starts to exceed ET again, surface layers get wetter, “convergent zero flux plane” develops - Zero Flux Plane graph (review the graph) - Percolation through Soil Horizons - Soil layering impact water flow when different horizons have different hydraulic conductivities (K) or pore size distributions - Water moving from coarse to fine-textured soil will be controlled by properties of the fine-textured soil, leading to a “perched water table” and maybe “throughflow” - Perched water table – an aquifer that occurs above regional water table in vadose zone - Complication: Preferential Flow - Matrix flow – water flow through an ordered soil matrix - Preferential flow – more rapid water flow that follows pathways that bypass the matrix as it infiltrates/percolates (Ex. cracks, root holes, worm holes)
-
Major Types: 1) Macropore flow 2) Fingered flow 3) Funnel flow 1) Macropores - Micropores = diameter ≤ 30 µm, relates to textural porosity of soil matrix - Macropores = diameter > 30 µm, relates to structural porosity around soil aggregates - Biological activity – root channels, worms, burrows - Geological forces – subsurface erosion, shrinkage, cracking, fracturing - Man-made – ploughing, drilling wells 2) Fingered Flow – unstable flow resulting from a higher “resistance” to water flow at certain locations in a soil - Caused by horizontal heterogeneity in matrix suction/soil properties, air entrapment or “water repellency” 3) Funnel Flow - Redirection of slow percolation caused by either an obstacle (clay, stone, ice, etc.) or a different texture soil lens (often a coarser texture) - Water in the Saturated Zone (Review diagram) - Aquifer – layer of consolidated or unconsolidated rock that is able to transmit and store enough water for extraction - Aquitard – geological formation that transmits water at significantly slower rate than aquifer - Aquiclude – geological formation that does not transmit water - Confined Aquifer – an aquifer bounded on both top and bottom by aquicludes - Semi-confined Aquifer – an aquifer bounded on one side by a semipermeable aquitard, and an aquiclude on the other side - Unconfined Aquifer – an aquifer without a confining layer above it o Water is recharged to the aquifer along its entire length - Water table – the upper boundary of the saturated zone in an unconfined aquifer - Energy in the Subsurface: Bernoulli - Moving water has 3 interchangeable types of energy (measured in Joules): 1) Kinetic energy – energy of motion 2) Potential energy – energy possessed due to an object’s position above a ref. Level 3) Pressure energy – energy related to pressure - Presuming no loss of mechanical energy due to friction, and presuming water is an incompressible fluid, Bernoulli’s Law: “For steady flow, the sum of the 3 interchangeable types of energy is constant (conservation of energy) mv2 + mgz + pV = constant - Bernoulli and Hydraulic Head - Divide Bernoulli’s Law by volume:
= ρv2 + ρgz + p
- Density and gravitational acceleration are almost constant, divide by ρ and g +z+
= constant
- Neglect the kinetic term because flow velocities so low in ground water, therefore Hydraulic head = Elevation head + Pressure head h = z + - Hydraulic head - Piezometer – tube/pipe with a short screen (opening) at its bottom - Pressure head – means of expressing soil water pressure on a gravitational potential energy basis, per unit weigh of water - Changing soil water pressure to a depth - Equal to the length of water in a piezometer above the screen - Elevation head – the elevation of the screen above an arbitrary datum - Hydraulic head – a measure of the total mechanical energy of the water - Equal to the sum of the Elevation head and Pressure head - Hydraulic Head and Flow Direction (textbook) - Water moves from higher to lower mechanical energy (hydraulic head) - Flow through Porous Media: Darcy (textbook) - Hydraulic gradient – the different in hydraulic head over a porous medium divided by the distance over which the different in hydraulic head is measured - Important the gradient is measured from the water-receiving end minus the waterdispatching end - What did Darcy find? The discharge at steady state was proportional to both hydraulic gradient and the area perpendicular to the water flow! - Darcy’s Law: Q = -Ksat × A × - Porosity vs. Hydraulic Conductivity (They are NOT the same!) - Ex. Sand = lower porosity + higher HC, Clay = higher porosity + lower HC - Homogeneity and Isotropy (textbook) - Homogeneous – K is the same everywhere - Isotropy – K is the same in all directions - Opposites are heterogeneous and anisotropic Lecture 10: Groundwater (continued) and Runoff - Darcy and Ohm (and Fourier and Fick) - Groundwater – movement of water in saturated zone - With Darcy’s Law, you just drop the AREA - Relationship between conductivity (how well something moves) and resistance (resistance to movement) is inversely related (C = ) - Fourier’s Law is some change of temperature over some conductivity of heat - Review Slide 3 (Exercise 3.7.1 in textbook) - Possible Exam Question!
- Recharge/Discharge Systems - Groundwater important to sustaining surface water - Even though there is no rainfall, groundwater maintains flow into rivers because of groundwater recharge - Equipotential lines – lines of equal hydraulic gradient in which groundwater flow lines are perpendicular (90°) to these lines - Streams are “fed” water even without rainfall for a while, known as exfiltration (the discharge of groundwater) - Groundwater Systems and Scale (pg. 101) - There are multiple scales of groundwater flows: - Local - Intermediate (hundreds of meters) - Regional (hundreds of km’s) - Regional and intermediate groundwater are important - Aquifer-Stream Interactions 1) Effluent (gaining) stream – difference between water table and stream surface is called the “seepage face” 2) Influent (losing) stream – surface water providing water to the groundwater 3) Influence stream with “perched stream” – an influent system that is not directly connected to groundwater because it is “perched” above water table 4) Flow-through Stream – simultaneously gains and loses water, mostly water dissolved through rock, and salts also moving into the system - Multiple types of interactions depend on climate and geology - Dissolved ions in water is what makes it conductive of electricity (ex. salt) - How does precipitation become streamflow? - Runoff - Rivers only take up a small portion of a watershed, but they carry the runoff of an entire watershed - Theories of how Rainfall becomes Streamflow (Runoff Generation) - Channel Interception - Hortonian Overland flow - Partial Area Concept - Subsurface Stormflow - Saturated Overland Flow and Return Flow - Macropore Flow - Groundwater Ridging - Variable Source Area Concept * Hydraulic Conductivity is usually a few m/day
- Terms and Definitions - Streamflow – a measurement of water (volume per time) passing a point in a stream - Runoff – the depth of water in a watershed corresponding to the measured streamflow; the process of water movement into streams (depth per time) - Hydrograph – a record of streamflow over time o Any graph with Q and t variables - “Old water” – water that is already stored in a watershed, and also includes the water in rivers - “Event water” – water input into a system during an event (ex. rainfall, snowmelt) - Channel Interception - Actual water falling directly into the channel - Initial rise in hydrograph is often associated with channel interception - Hortonian Overland Flow (HOF) - HOF is a situation where rainfall increases and water cannot infiltrate the ground quickly enough, which results in overland flow - Input rate > infiltration capacity (rainfall intensity exceeding rate of infiltration) - The whole watershed will overflow and entire watershed is streamflow (not just the channel) - Similar idea with a parking lot flooding because infiltration is practically ZERO - Partial Area Concept (PAC) - PAC almost the same as HOF, except it happens on a small portion of the rivers in a watershed (HOF assumes there are vast sheets of water coming into a river) - Subsurface Storm Flow (SSF) - If you have HOF, then you have OLD and EVENT water mixing to produce new water - Most hydrographs are OLD water, not a large portion of NEW water of runoff - Saturation Overland Flow (SOF) and Return Flow - SOF makes a little more sense - Control from above, where water is inputted and water storage is increased where water rises to the surface, the water table intersects the surface so groundwater comes up - Looks like infiltration flow, but stick a well into the ground and the water will come up - Ground Water Ridging (GWR) - GWR is one way to make SOF come up (for the watertable to come up) - Capillary fringe is relatively saturated and close to being a water table, and only a relatively small amount of water is needed to cause a rise in water - Groundwater tables tend to be near the surface near water zones - Macropores and Quick Subsurface Flow - Animal burrows - Dead tree and plant roots - Worms - These tunnels are visible but hard to quantify or study
- Variable Source Area Concept - Similar to SOF where areas near sources of water tend to get wetter, and after rainfall you get some more saturated areas, and over time these saturated areas expand - Majority of shaded areas (on the diagram) are areas that intercepts rainfall and give quick means for water to be input into the river system Lecture 11: Runoff and Streamflow - Importance of Understanding Streamflow dynamics - Water Supply – the huge supply such as lakes which are mostly fed by rivers - Important to understand the inflows and outflows to track the supply - Water Quality – the constituents within water in a stream are controlled by the pathway water takes to get to a stream - Flood Prediction – understanding past streamflow records allow us to make educated choices about certain actions Ex. determining the necessary height of a dam, warning of potential future floods - Factors affecting runoff 1) Watershed size – the bigger the more water in it, and streamflow generally decreases downstream 2) Topography – how hilly or how flat, affects how water gets into a stream - Runoff always occur downhill, perpendicular to contour lines 3) Shape – flow from various parts of watershed are affected by the shape of the watershed, such as long-narrow or circular 4) Aspect/Orientation – which way it is pointing is important for energy, orientation, latitude, slope, etc. 5) Geology – affects soil formation, thickness, slope/gradients, drainage, made watershed boundaries 6) Soil – soil properties can affect hydraulic parameters - Measuring Streamflow – it is done physically or mathematically - Discharge = velocity × cross-sectional area Q = vA (because L/T × L2 = L3/T = m3/s) - Velocity-Area Method - Measuring Velocity 1) Using a tool while in the water to measure how fast (velocity) water is pulling you 2) Using a windvane-like device and measure how many clicks over a time period 3) Yellow tail spins to measure revolution to get downfall velocity - 6/10 depth vs. 2/10 and 8/10 depth methods - Depending on the depth of the stream - When stream depths < 0.75 m, average velocity assumed to be about 6/10 depth below surface of water (4/10 above bottom) - In deeper streams, average measurements made at 2/10 and 8/10 depths
- Velocity-Area Method - You take the stream and break it into specific sections that are more easier to measure because velocities will be different - Representative velocity is some point in the middle of each line, add them all up to get your total velocity of discharge (middle of those two dashes on each line) - The Rating Curve - The Gaging Station - Basically it is a big well with instruments that record water levels, and as water levels go up, the well will go up as well - Dilution Gauging - A chemical method that adds a tracer in water (such as salt, dye that creates colour) - Concept is to add the tracer at some location at a known rate, and at a certain distance, that tracer will mix itself with water, and at some point the river will be well-mixed - More accurate than area-velocity QCu + QiCi = (Q + Qi)Cd Q = Qi - Weirs and Flumes – restricts cross-sectional area of streams - Weir – restricts depth to flow over a notch that is raised above the stream bed - Generally like a dam, where water flows over a v-notch - Flume – restricts both depth and width - More expensive to install, but self-maintaining - Flow Over a Weir (No need for a rating curve) Q = 1.18 × CdB × h1.5 - The Hydrograph (refer to textbook page 244) - Tells alot by its shape as to what is going on - Relatively a discharge over time, starts to go up with flow - Antecedent flow rate – before rainfall - Time of rise – the different of time lag, basin lag - Peak flow - Falling limb - Hydrograph separation line - Groundwater recession - Hydrological Regimes - Hydrological Regime – the entire state of water movement in a watershed - Runoff regime – the characteristic response of runoff in a watershed given its climate and geography - Important Runoff Regimes in Canada - Nival Regime – snowmelt dominated (Canada mostly covered by this) - Occurs around march or april when snowmelt occurs - Pluvial Regime – rainfall dominated - Glacial Regime – glacier-melt dominated
- Similar to nival regime, you get peakflow around spring - But the difference is that the peak is shifted intot he summer because these areas warm up later (delayed because of their geography) - However, peakflows remain similar to nival regimes, just shifted Lecture 12: Flood Analysis and Water Quality - Hydrograph Separation - The point is to distinguish “baseflow” from “stormflow” (arbitrary) a) Constant discharge method b) Constant slope inflection point method c) Concave curve inflection point method - Runoff Ratio of Coefficient (RC) - Measures the amount of precipitation input that is observed as discharge -
RC =
- What is a Flood? - An enormous flow down the river - Many ways to get a flood, such as a huge tide, a big bay can move large amounts of water can also flood - Floodplains – areas known to flood often 9and homes are built on them) - Flow Duration Curves - Constructing a Flow-Duration Curve (IMPORTANT, need to know how to read it!) - Weibull Formula (review example on slide 9) - Calculates return periods (T) or probabilities of exceedence (P) -
T=
P=
- Flood Probability Short Cuts - Probability that an RP-return period flood will be exceeded in ALL of next n years = [ 1 RP]n - Probability that an RP-year return period storm will be exceeded at least once in n years = 1 – [ 1 – 1/RP ]n - Probability that the next time an RP-return period flood will be exceeded is n intervals from now = [ 1 – 1/RP ]n-1 × 1/RP - Limitations of Frequency Analysis - Review slides 15 to end
