Physics of Aquatic Systems

Transcription

1 Physics of Aquatic Systems MVEnv3 Physics of Aquatic Systems One of four main lectures in Environmental Physics: Atmosphere, climate, terrestrial and aquatic systems 1. Introduction (Properties of Water) Werner Aeschbach Hertig Mi Main focus: Lakes, Lk groundwater, isotope hydrology hd This lecture builds on fundamental environmental physics (e.g., fluid dynamics) of the lecture MKEP4 For details, updates and lecture notes see heidelberg.de/institut/studium/lehre/aquaphys/mvenv3.html Overall Contents I Part I: Aquatic Physics 1. Introduction (role and physical properties of water). Density stratification and flow in lakes and oceans 3. Turbulent flow in surface waters 4. Turbulent transport in surface waters 5. Energy flow in surface waters 6. Gas exchange 7. Flow and transport in groundwater Overall Contents II Part II: Isotope Hydrology 8. Introduction to Isotope Hydrology 9. Stable Isotopes 10. Tritium and 3 He 11. Dating of Young Groundwater and Modeling 1. Dating of old Groundwater 13. Noble Gases and Paleoclimate Contents of Session 1: Introduction Definition of "Physics of Aquatic Systems" Compartments of the hydrosphere 1.1 The global hydrological cycle Water problems as a motivation for water research 1The 1. role of water in the environment Physical properties of water 1.3 Specific and latent heat, vapour pressure 1.4 Heat conductivity, diffusion, viscosity What is "Physics of Aquatic Systems"? Study of physical conditions and processes (e.g. stratification, flow, transport, mixing, heat/gas exchange) in natural systems containing liquid water (e.g. lakes, ocean, groundwater) Related Disciplines, Subdisciplines: Physical Oceanography and Limnology Hydro(geo)logy and soil physics Meteorologyand (paleo)climatology For comparison: What is Hydrology? Study of the global water (hydrological) cycle, especially water on the continents, above, on, and below the surface Classical hydrological systems: Catchments of rivers/aquifers Physical aspects: Water balance, water fluxes Chemical, biological, and technical/sociological aspects Engineering aspects: water supply, flood protection, etc. 1

2 ET(t) Hydrologic Water Balance Hydrological system: reservoir with input P (precipitation) output R (runoff) output ET (evapotranspiration) Continuity/Mass conservation:input Output Change in storage P R ET ds dt Simple equation, but individual terms are difficult to quantify Isotopes may help Part of this lecture Water on Earth All water on Earth: km 3 Sphere with R 700 km thereof 3 % fresh water: ~ 10 6 km 3 Sphere with R 00 km Saltwater and Freshwater Water in env. compartments (blue: Hydrosphere) volumes in 10 3 km 3 Saltwater: 1'365'000 thereof Oceans: 1'365'000 Salt lakes (Casp. Sea): 80 Compartments of the Hydrosphere Freshwater: 35'000 thereof Ice: 4'000 Groundwater: 10'800 Soil water: 70 Lakes: 110 (Lake Baikal 3) Atmosphere: 16 Rivers: Biosphere: from Mook, 001 Groundwater and Surface Water 1.1 The Global Hydrological Cycle Groundwater: By far largest freshwater reservoir partly difficult to access Usually clean (drinking water) slow renewal Surface water: Rather limited Resource, esp. in arid regions Easily accessible Frequently polluted fast recycling Oceanography Limnophysics Hydrology Soil Physics Hydrogeology rometeor. 8: Trenberth et al., 007, J. Hydr

3 Global Water Budget and Cycle Fluxes in 10 3 km mm 1030 mm Continents Oceans km km Whole Earth evaporation/precipitation flux: km mm Water Balance of the Continents Component Volume flux [km 3 /a] Input Precipitation Output "Blue" and "green" water Evapotranspiration Ecosystems green water - Grassland % utilised - Cropland Runoff.000 blue water - Withdrawals % utilised Sum Output renewable water resource:.000 km 3 /a realistically accessible: km 3 /a present utilisation: 30 % Distribution of the Water Resources Water scarcity is regional, not global. Global Distribution of Water Resource Stress DIA/Q Ratio of total (Domestic, Industrial, Agricultural) water demand to total sustainable water supply (river discharge Q) Oki and Kanae, 006. Science 313: Vörösmarty et al., Science, 000 Global Water Use Irrigation Irrigated agriculture produces % of the world's food on 0% of the agricultural area accounts for 70% of the water withdrawals (3.000 of the available km 3 /a) regionally overutilises surface and ground water Hidden problem: non sustainability 3

4 Unsustainable Water Use: Drying Lakes Unsustainable Water Use: Drying Rivers Aral Sea Lake Chad The Yellow River (Huang He) nowadays falls dry for about 4 months each year. Unsustainable Water Use: Falling Water Tables Unsustainable Water Use: Falling Water Tables Central Valley CA, USA North China Plain San Francisco Groundwater Atlas of the US Foster et al., 004. Hydrogeol. J. 1: The Role of Water in the Environment Water permeates all spheres of the environment important medium for transport (heat, substances) Basis of life most abundant molecule in the biosphere Role of water in the climate system Ocean: Heat storage and transport Water vapour: greenhouse gas, clouds, latent heat Snow, ice: high albedo Role of the Ocean in the Climate System Facts on the ocean: Area: km (70 % of Earth's surface) Volume: km 3 mean depth 3800 m Mass: kg ( 80x m atm ) largest heat reservoir largest mobile CO reservoir large surface with low albedo 4

5 The Hydrologic Cycle in the Climate System Warming Accelerates the Water Cycle H O e [mbar] %/ C T [ C] Water vapour saturation pressure depends strongly on temperature Theoretical increase of water fluxes by about 7% per C Actual changes: Climate models: < 3%/ C Data: 6 %/ C Wentz et al., 007. Science 317: IPCC, AR4, 007 water cycle Predictions for Precipitation Physical Properties of Water Precipitation compared to IPCC, AR4, 007 ( Property Comparison Importance, consequences Specific heat Highest of all solids and 4180 J kg 1 K 1 liquids except liquid NH 3 Heat transport by water movement, heat buffering Heat of fusion Highest except NH 3 Thermostatic effect at freezing point J kg 1 Heat of evaporation J kg 1 Highest of all substances Heat and water transfer in the atmosphere ρ max at T > T freezing (~4 C at 0%, 1 atm) anomalous Density stratification of lakes, facilitates freezing ρ solid < ρ liquid anomalous Ice floats on water, freezing only at surface, weathering Surface tension Highest of all liquids Drop formation, capillary forces, soil water retention, cell physiology Dissolving power Very high Transport of dissolved substances Dielectric constant Highest of all liquids except H O and HCN High dissociation of dissolved salts Molecular Origins of the Properties 1.3 Specific and Latent Heat, Vapour Pressure H O Molecule: H O H with o binding angle polar hydrogen bonds! 5

6 Temperature Dependence of some Properties Saturation Vapour Pressure Description of a phase transition 1 by the Clausius Clapeyron equation: dp L1 dt T v v ( ) 1 L: Latent Heat v i 1/ρ i specific volumes Phase diagram of water For vapour water: v v w << v v and RT vv p Thus: dp Lp dt RT mit R D R/M W J kg -1 K -1 Saturation Vapour Pressure Saturation Vapour Pressure From Clausius Clapeyron: dp p s s LdT R T Integration gives ( ) ( ) p T L 1 1 s ln p T R T T s 0 0 mbar] e [ 30 0 Magnus: 7.5 T[ C] 38+ T[ C] es ( T) hpa 10 L 1 1 ps( T) p0 exp R T T 0 10 e.g.: T 0 0 C, p mbar, L J kg 1 In practice: Magnus equation ( ) 7.5T[ C] 38+ T[ C] ps T hpa T [ C] 1.4 Heat Conductivity, Diffusion, Viscosity These properties are related to molecular diffusive transport unordered motion of molecules (water or dissolved substances) leads to flow against gradient 1. Fick's First Law: Flux density given by 1 D: 3 D: c jdif,x D x j -D c dif Heat Conduction as "Temperature Diffusion" Heat conduction: Flux of thermal energy 1 D: j temperature "heat concentration" th γ x dq c dt p V ρ J J K intensive ms smk m extensive Jm K Heat conduction as "temperature flux" Fick I: jt DT x K m m K s s m D γ c ρ T p jt jth cpρ γ: thermal conductivity D T γ/c p ρ: thermal diffusivity 6

7 Viscosity Shear stress and momentum flux: Shear flow, i.e. velocity gradients, lead to shear stress. e.g. shear stress in x direction due to gradient of v x in z direction: τ xz v x μ z τ xz can be interpreted as a flux density of x momentum vx vx τ xz μ νρ ν ( ρv x ) diffusive flux of x z z z momentum in z direction dynamic kinematic momentum ν [m /s]: Diffusion coeff. viscosity density z v x Diffusion for Substances, Momentum, Temperature Fick's First Law: Substances: Momentum: Heat: c v x j D τ x xz νρ z Fick's Second Law: Substances: Momentum: Heat: t x x c j c D v 1 τ v t ρ z z x xz x ν jt DT x D t T T x Diffusion Coefficients in Water Summary Property being transported Dissolved molecules Transport parameter symbol Order of magnitude [m /s] Diffusion coefficient D 10 9 Heat Thermal diffusivity, D T, κ 10 7 (Temperature) Temp. conductivity Momentum Kinematic viscosity ν 10 6 Aquatic Physics looks at physical processes in aquatic systems The hydrological cycle is a central process in the environment The hydrosphere is an essential part of the climate system Humanity's use of water is about 30 % of the available resource In arid regions, over exploitation occurs (drying lakes, rivers, etc.) Physical properties of water are quite extraordinary High specific and latent heat are important for the climate Vapour pressure strongly increases with temperature Molecular diffusion: transport of substances, heat, momentum Diffusivity for momentum/heat much higher than for substances 7