Fundamentals and Principles of Hydrology PDF

MHSE02: Climatology and Hydrology Part 2: Hydrology Fundamentals and Principles of Hydrology Department of Hydrology Bergstraß...

MHSE02: Climatology and Hydrology Part 2: Hydrology Fundamentals and Principles of Hydrology Department of Hydrology Bergstraße 66 West floor 01069 Dresden Version 2.3.2 Last modified October 13, 2024 PD Dr. habil. Thomas Wöhling © These lecture notes are provided as part of the MHSE02 module of the Master Course Hydro Science and Engineering, at the Chair of Hydrology, Institute of Hydrology and Meteorology, Technische Universität Dresden (TUD), Germany. The lecturer holds the exclusive rights to reproduce, distribute, publish, modify, and/or license the script, course slides, exercise sheets, and all other accompanying course materials. Distribution of these materials is not permitted. Index Fundaments and Principles of Hydrology Index 1 Objectives and Introduction.................................................................................................. 4 1.1 Introduction............................................................................................................................. 4 1.2 Scope of hydrology.................................................................................................................. 4 1.3 Work fields of hydrology......................................................................................................... 4 2 The Global Hydrological Cycle................................................................................................ 4 3 Water Balance Equation........................................................................................................ 5 3.1 Water balance components.................................................................................................... 5 3.2. Water and heat balance............................................................................................................... 6 4 The Catchment...................................................................................................................... 6 5 Description of Hydrological Processes.................................................................................... 7 5.1 Hydrological processes & systems.......................................................................................... 7 5.2 Hydrological Modelling............................................................................................................ 7 5.2.1 Model scales........................................................................................................................ 7 5.2.2 Model concepts................................................................................................................... 8 5.2.3 Model calibration................................................................................................................ 9 6 Precipitation......................................................................................................................... 9 6.1 Formation of precipitation...................................................................................................... 9 6.2 Precipitation measurements................................................................................................. 10 6.3 Analysis and correction of precipitation measurements...................................................... 10 6.4 Spatial interpolation methods............................................................................................... 12 6.5 Extreme rainfall..................................................................................................................... 13 6.6 Snow and snowmelt.............................................................................................................. 14 7 Runoff................................................................................................................................. 17 7.1 Runoff measurements........................................................................................................... 17 7.2 Hydrograph analysis.............................................................................................................. 19 7.3 Floods and Droughts.............................................................................................................. 20 7.3.1 Floods............................................................................................................................ 21 7.3.2 Droughts........................................................................................................................ 21 7.4 Runoff components............................................................................................................... 22 7.5 Runoff formation................................................................................................................... 23 2 Index Fundaments and Principles of Hydrology 7.6 Runoff concentration............................................................................................................ 24 7.7 Flow routing........................................................................................................................... 26 7.8 Rainfall-runoff modelling....................................................................................................... 26 8 Evapotranspiration.............................................................................................................. 27 8.1 Evaporation........................................................................................................................... 27 8.2 Transpiration......................................................................................................................... 28 8.3 Interception........................................................................................................................... 28 8.4 Evapotranspiration - measurement and estimation............................................................. 30 9 Regional Aspects of Hydrology............................................................................................. 32 9.1 Arid Areas.............................................................................................................................. 32 9.2 Humid Tropics........................................................................................................................ 33 9.3 Polar regions.......................................................................................................................... 34 3 Index Fundaments and Principles of Hydrology 1 Objectives and Introduction 1.1 Introduction  A quarter of the world's population does not have access to safe drinking water  Almost half of mankind lacks adequate sanitation  Poor water quality and lack of hygiene are among the primary causes of death and disease  Scarcity of water, flood and drought, poverty, pollution, inadequate treatment of waste and lack of infrastructure pose serious threats to social and economic development, human health, global food security and the environment Hydrological science has a central role 1.2 Scope of hydrology  All hydrological processes are non-stationary.  All hydrological processes are interconnected or linked with other natural systems. Two physical laws are of fundamental importance for the movement of water on the land surface and in soils/aquifers:  Conservation of mass  Conservation of energy These laws form together with other laws and/ or empirical relationships the basis for hydrological models. 1.3 Work fields of hydrology The hydrological cycle  Research on interconnections of hydrological processes with chemical, physical and biological processes  Systematic analysis of hydrologic phenomena in order to improve the theoretical hydrologic foundation and hydrological methods  Transport processes in the SVAT system  Runoff generation processes Measurement and analysis of hydrological processes  Analysis of hydrological data  Improvement of measurement networks  Identification of suitable modelling concepts and their formulation 2 The Global Hydrological Cycle  Solar energy and gravity are the driving forces of the global hydrological cycle  closely linked to the heat balance of the planet  interconnected with other transport cycles  energy transport by evaporation and condensation processes  local and regional processes  larger scales global hydrological cycle  Significance of global considerations: analysis and assessment of human activities on a global scale, e. g., climatic change Dynamics of the hydrological cycle  Spatial and temporal distribution of water on Earth highly variable (hydrology = non-stationary)  mean residence times in the compartments of the hydrological cycle vastly different 4  Fundaments and Principles of Hydrology Natural pollution control  Distillation in the atmosphere  Physical filtering, chemical and biological transformation processes in soils and surface waters Water reservoirs (compartments of the hydrological cycle)  Largest reservoir: Oceans  Largest reservoir of fresh water: Ice shields of the arctic regions  Groundwater  Unsaturated soil  Atmosphere  Lakes, rivers, plants, animals, … Water and heat  Transport of energy by oceans, exchange of energy between surface and deep sea water (thermohaline circulation)  Snow cover of the land surface (up to 50%) and oceans (≈10%) reflect radiation (global albedo)  Smoothing of temperature variations by freezing and melting of ice 3 Water Balance Equation  Quantification of the hydrological cycle for a given area and time step  Precipitation P, evapotranspiration ETR, runoff R and storage ΔS from the water balance of a watershed (1 mm/d equals 1 l/m²/d)  Water balance is calculated for a defined area (usually a watershed) and a defined period (often the hydrological year which starts at the first of November in middle Europe). Balances:  Global yearly average: P = ETR [mm/a]  Yearly average for the land surface: P = ETR + R [mm/a]  Land surface for shorter periods: P = ETR + R + ΔS [mm/a]  Arbitrary area at the land surface (excluding human intervention): P = ETR + R + ΔS - SWin - GWin + GWout [mm/a] ΔS can only be neglected for yearly average values (at most) Storage: Ice, snow, surface water, soil, groundwater Examples: Germany: P 783 = ETR 513 + R 270 [mm] South America: P 1600 = ETR 910 + R 685 New Zealand: P 1650 = ETR 660 + R 990 3.1 Water balance components P... Precipitation SW in... Inflow surface water/ SW out…Outflow surface water GW in... Inflow groundwater GW out…Outflow groundwater ETR... Evapotranspiration ∆S... Storage change 5  Fundaments and Principles of Hydrology 3.2. Water and heat balance The energy input to the earth system drives the hydrological cycle Heat balance Water balance Rn = G + H + LE [W/m² or kJ/m²/s] P = R + ETR + ∆S [mm/Δt] Rn … Net radiation, P... Precipitation G... Soil heat flux R... Runoff H... Net sensible heat flux ∆S... Storage LE... Net latent heat flux ETR... Evapotranspiration  Solar (short wave) radiation 341 W/m²  Evaporation in mm/Δt and energy transfer in kJ/m2/Δt are linked by the latent heat of vaporization 2448 kJ/kg  2448 kJ/m² this amount of energy vaporizes 1mm = 1 l/m² of water Evapotranspiration: Link between water and heat balance is an important component of both the heat balance (LE) and water balance (ETR) 4 The Catchment Catchment  open hydrologic system: in- and export of matter and energy (precipitation, deposition, runoff, erosion) At the boundaries: analysis of interactions with neighbouring systems A catchment is always assigned to a cross section of a river (often a river gauge). The horizontal projection of the area of the catchment is called the drainage area. The total runoff (surface runoff as well as groundwater) is generated by this area. Proper delineation of the surface and subsurface catchment boundaries is of fundamental importance particularly for small catchments. Types of watersheds  Surface water catchment → drainage area: Is delimited by divides - using a contour map (DEM) with an appropriate resolution the divides are drawn always perpendicular to the contour lines starting from the chosen cross section.  Groundwater catchment → aquifers: Determined by (the stratigraphy of) geological formations and impermeable layers, aquifers form a subsurface watershed. Surface and subsurface catchment boundaries may differ. Groundwater divides separate different aquifers. Vertical structure: Horizontal structure:  Surface system  geomorphological & topographical criteria (soil types, vegetation, rivers and lakes)  Land cover  Soil system  Soil types  Aquifer system  River network 6  Fundaments and Principles of Hydrology 5 Description of Hydrological Processes 5.1 Hydrological processes & systems Hydrological processes: transient movement of water. Changes of pressure, temperature, phase or density may occur. Hydrological processes take place at different spatial and temporal scales. Investigations are usually conducted on the catchment scale. The surface water boundary of a catchment (divide) is often an artificial boundary. The most important hydrological processes  Precipitation, P  Evapotranspiration, ETP o Interception o Evaporation o Transpiration  Runoff, R o Surface runoff o Runoff from soils o Runoff from groundwater  Infiltration, I  Storage, S o Soil storage o Groundwater storage o Storage in rivers and lakes o Interception o Surface storage o Snow storage Runoff generation 1. Runoff formation in the basin (land phase) 2. Runoff concentration (discharge formation in the stream channel system, channel bed phase) 3. Flow routing process in the channel system (flood propagation or wave attenuation phase) 5.2 Hydrological Modelling 5.2.1 Model scales  Models are tools for analysis and simulation  Models describe relevant hydrological processes → As simple as possible and complex as necessary!  Model purpose determines what is relevant Different temporal & spatial scales for different questions (model purposes):  Q: How much sea-level rise by 2050? - global scale energy budget, annual averages - global greenhouse gas emissions - atmospheric energy retardation - temperature rise, glacial melt  Q: How vulnerability are fir trees to drought? - local scale (E, θ, C, N), days / hours - climate drivers (Rn, T, v, … P) - interception, troughfall, infiltration, soil water movement, - root water uptake, photo-synthesis, assimilation & respiration  Q: Flood vulnerability - catchment  Q: Self-cleaning mechanisms of rivers: - river reaches  Q: Productivity of crops - field, soil column 7  Fundaments and Principles of Hydrology Relevant scales in time and space 1 m² 100 m² 1 ha 1 km² 10² 10*10³ 1 Mio. km² 1m 10 10² 10³ m 10 km 10² 10³ km  Identification of scale dependent relationships  Consideration of sub scale effects 5.2.2 Model concepts Model Types  Empirical models (black box) e.g., the hydrological systems approach: Data-driven modelling concept. It relates input to output on a temporal basis. The hydrological process is approximated by a mathematical function (system operator / transfer function). o Advantages: good reproduction of system behaviour, easy application, very fast o Disadvantages: not valid beyond calibration data range, fitting required, typically not transferrable, no hypothesis testing possible, no process understanding  Conceptual models (grey box) Use of physical concepts together with empirical components. o Advantages: smaller CPU times, variable spatial resolution o Disadvantages: calibration required, not valid beyond calibration data range  Physically based models (white box) Based on general physical laws for the description of hydrological processes. o Advantages: Measurable parameters, validity beyond the scope of historical time series o Disadvantages: high data requirements, sub scale effects, large CPU times  Stochastic models Estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs. Approach: Monte-Carlo Methods, MCMC. o Advantages: assessment of uncertainty o Disadvantages: many model runs required, large CPU-time requirements Solution methods Spatial representation Temporal representation - Analytical - lumped - steady-state - Numerical - distributed - event - Hybrid - coordinate system - transient 8  Fundaments and Principles of Hydrology The modelling process 1) Formulation of the research questions and hypotheses 2) Conceptualization type of information required, accuracy, time intervals,.. purpose 3) Model selection and development purpose(!), data availability, run-time, alternative models? 4) Parameter estimation (calibration) formulation of the objective function search method: manual, local/global, stochastic 5) Model evaluation (testing) independent data 6) Uncertainty assessment 7) Model application Structure of hydrological models and their uncertainty sources 5.2.3 Model calibration  Almost always required to estimate uncertain or empirical parameters → optimization problem  Comparing data with model simulations (objective function) and adjusting parameters to minimize the difference between the two  Choice of objective function, data type and quality determines model’s performance  Optimization techniques: manual calibration (try-and-error), local (linear) optimization, global search methods 6 Precipitation 6.1 Formation of precipitation  Most important input to water balance calculations  rain (liquid water), snow, hailstones, sleet, freezing rain  characteristics: o amount of rainfall/event o reoccurrence period o duration and intensity 9  Fundaments and Principles of Hydrology Different meteorological situations lead to different types of precipitation  Convective rainfall uplift of warm moist air leads to condensation by adiabatic cooling (typical: equator) short duration, limited spatial extend, high intensity  Orographic rainfall (mountains) uplift of moist air at topographic barrier  cooling  rainfall wind speed, elevation and steepness of barrier determine intensity and duration of rainfall often orographic effects are results of convective or frontal mechanisms  Convergence (frontal and cyclonic convergence) Poleward energy transfer, extratropical front development, uplift in low pressure areas, warm front: warm wet air meets cold dense air – uniform moderate intensities, cold front: cold dense air moves under warm wet air - high intensities 6.2 Precipitation measurements  Rainfall depth [mm] observed depth for a given Δt, hourly, daily, monthly  Rainfall intensity depth per Δt [mm/h] [mm/day]  Rain yield factor [l s-1 ha-1] Parameter for calculation of resulting stormwater volumes Point measurement  small sample of the rain field  Rain storage gauge: averages, no recording of extreme values  Mechanical rain gauge (e.g., Hellmann, tipping-bucket): daily/weekly resolution  Automatic rain gauges (weight-recording, optical): low maintenance, autonomous, for mountainous areas, measurement sites difficult to access Monitoring of the spatial distribution of rainfall  Ground radar and remote sensing products  Extrapolation of point measurements (c.f. section 6.4) Measurement errors Systematic errors  standard conditions (height, obstacles)  change of instruments, change of location  evaporation  splashing, wetting  wind, snow Random errors  Error in reading 6.3 Analysis and correction of precipitation measurements Homogeneity A time series is homogenous, if the variations are caused by meteorological reasons only.  Systematic changes which are not caused due to meteorological reasons: o Micro climate: houses, streets, vegetation o Measurement instruments o Observer  Documentation of the station history  Systematic changes caused due to meteorological reasons: o Anthropogenic influences: irrigation, hydroelectric power plant, storage dam o Sedimentation, natural disasters, climate change (slow changes in hydrological regime ) 10  Fundaments and Principles of Hydrology Homogeneity tests:  Absolute tests consider only one time series  Relative tests: o include different time series o use of reference time series o preferred over absolute tests o Examples:  Abbe – Test (high-pass filter, sign and magnitude of deviations from average),  Double mass curve  Autocorrelation method Double mass curve: What determines whether the change in the slope is significant?  The trend has to continue at least 5 years  Statistical significance (tests of variance and covariance) To yield a consistent time series (annual average):  Exclude data before the change if you can  Else, correct data before change: multiply by K   only if clearly associated with changes in the measurement conditions   not if climatological change Consistency Consistency tests are hardly possible for precipitation data.  Correction of precipitation data Discharge data can be tested for consistency. Correction All precipitation measurements have systematic errors!  Wetting- and evaporation error; loss rate per precipitation day considering the number of precipitation days with more than 0.1 mm rainfall (measurement instrument error)  Wind induced error; classification according to precipitation type and exposition of measurement station; depending on wind velocity and quantity of precipitation  Total error = wetting error + evaporation error + wind error  Other sources of errors: fog, mist (condensation), frost (e.g. Ore Mountains)  The measurement error is large for: o Specific events (up to 75%) o Snowfall (up to 90%) o Impacts on the measurements by obstruction (trees, buildings), varying observers, change of location Example: Hellman gauge  Wetting error: + 5-10 %  Evaporation error + 1-3 %  Wind induced error + 2-15 % (rain), +15-55 % (snow)  Total error: up to >50 % Correction of precipitation data using the method by Richter (1995) Wetting- and Evaporation Error  Calculation of losses from wetting and evaporation for days with ≥ 0.1 mm precipitation [mm/d] … mean loss 11  Fundaments and Principles of Hydrology … percentage of wetting and evaporation losses … mean monthly sum of precipitation … number of days with precipitation Wind-Induced Error  Influences and processes, which affect the measurement of precipitation with conventional rain gauges, e.g., wind drift → instrument causes turbulence; divert precipitation (impact of wind direction)  Estimation of the wind error by precipitation type: o liquid o snow o mixed precipitation (snow and rain)  … and by the exposition of the met station: o exposed to wind (distance between gauge and vegetation or buildings > 10-20 times of the height of the obstruction) o little sheltered (5-10x height) o moderately sheltered (5x height) o strongly sheltered (2-5x height) Data Supplementation:  Supplemented data shall not cause inhomogeneity in the time series  The method of supplementation should include information from as many stations as possible  Well-correlated stations should be given a larger weight Methods for Data Supplementation  Average: e.g., monthly means of current and past years  no consideration of other stations  Station average: e.g., mean from surrounding stations  more robust, but stations not weighted  Regression:  for relatively few values missing  Normal-ratio method:  weighting by annual-average precipitation  Inverse distance weighting:  weighting by distance to other stations  (External drift) kriging:  weighting by distance, elevation, … 6.4 Spatial interpolation methods  Rainfall is a space-time varying process  For hydrologic tasks spatial averages may be required  Interpolation methods: Arithmetic Mean:  if no other information (e.g. location) available  equal weights to all stations 1 n P= ∑ pi A i=1 Thiessen Polygon:  locations of stations are known  ai determined as area bounded by perpendicular bisectors 1 n P= ∑ ai pi A i =1 12  Fundaments and Principles of Hydrology Isohyetal method:  drawing contour lines of equal precipitation  high data requirement 1 n P= ∑ ai pi A i =1 Inverse distance weighting:  surrounding stations are weighted by their inverse distance  Impacts of catchment topography on the rain field not considered n ∑P d −1 i xi P = i =1 x n ∑d −1 xi i =1 Geostatistical methods - Kriging:  Ordinary kriging - considers the spatial variance of P - interpolated values are modelled by a Gaussian process - gives the best linear unbiased prediction of the intermediate values - assumes that the realizations of the variable is a stationary random field (which is for precipitation often not the true)  External Drift Kriging - considers dependencies of the interpolation variable to other variables or measurable properties (cross-correlation), e.g. elevation  Internal Drift Kriging Integrates e.g. spatial trends of the interpolation variable (autocorrelation)  Model choice is subjective and – thus- the results of the interpolation 6.5 Extreme rainfall PMP – Probable Maximum Precipitation  Objective: calculation of Probable Maximum Flood (PMF)  Def. WMO: theoretically the greatest depth of precipitation for a given duration that is physically possible over a given size storm area at a particular geographical location at certain time of a year  Is there an upper limit for rainfall volumes for a given duration? o Storms: physical upper limit o maximum storm + saturated moisture in the catchment + meteorological reasoning  Estimation based on: o Storm area: estimation of PMPs for various durations and areas in a large region o Catchment location: to estimate the PMP for a given duration and area (e.g., reservoir design)  Different methods Local estimation of storm rainfall  design and risk analysis based on exceedance probability (= inverse of return period) and not on PMP/PMF  Aim: estimation of rainfall depth with given return period for various storm durations o Depth-Duration-Frequency (DDF) analysis o Intensity-Duration-Frequency (IDF) analysis (intensity = depth / duration) 13  Fundaments and Principles of Hydrology  Data analysis of rainfall records a) Annual series b) Peak over threshold Storm rainfall: Depth-Duration-Frequency-Curve DDF  Different characteristics e.g. short durations – high intensity  Frequency analysis to compute rainfall depth for a given duration and a given return period o Data analysis, e.g., annual maxima of rainfall depth for given duration o Derive empirical cumulative probability density function (cdf) o select theoretical probability distribution (EV1, EV2, Gumbel…) o estimate parameters of the theoretical distribution (fit the distribution) o test of goodness of fit (Kolmogorov, Chi-square test) o Compute quantiles for each duration and selected return period o Estimate of parameters of DDF curve for selected return period  Example Gumbel distribution:   x − u  F ( x ) = exp  − exp  −    α  Method of moments: 0.5772 ∞ µ x = ∫ x ⋅ f ( x ) dx =u + γ e ⋅ α −∞ ∞ π2 σ x2 = ∫ ( x − µx ) ⋅ f ( x ) dx = α2 2 −∞ 6 α = 6σ x /π u = µx − γ e α - exceedance probability 1 – F = 1/R - return period, R 1 R= 1− F - rainfall for a given return period and duration:    R − 1   x = u + α − ln − ln      R   6.6 Snow and snowmelt Constituents of snow:  Snow crystals (~ 10 - 40 Vol.%)  Air (~ 60 - 90 %)  Liquid water (~ 0 - 30 %) below 0°C 2-phase system, above 3-phase system 14  Fundaments and Principles of Hydrology Properties:  Snow height in [cm]: point measurement, spatially heterogeneous  Water equivalent [mm]: melting of a defined volume of snow  Specific water content [mm/cm]: water height / 1 cm snow  Density [kg/dm³]: mass per unit volume o snow freshly fallen ~ 0.05 – 0.17 o powder ~ 0.1 – 0.2 o settled snow ~ 0.35 – 0.6 o firn ~ 0.5 – 0.85 Water equivalent of the snow cover: [g/cm²]  [l/m²] = [mm]  spring flood forecasting Energy balance of the snow cover: ∆S = RS + RL + H + LE + HR + G ∆S... net rate of energy exchange RS... short wave radiation input = f (albedo a) RL... long wave radiation exchange H... exchange of sensible heat LE... exchange of latent heat HR... heat input by rain G... conductive exchange of sensible heat with the subsurface Mass balance of the snow cover: Pr... precipitation (snow or liquid) Mo... melt water output LEa... evaporation of snow or condensation Processes: Accumulation  Snowpack metamorphism Warming  Ripening  Melting  Output 4 Mechanisms of Snow Metamorphism  Compaction by gravity  0,002 – 0,05 g cm-3 day-1  Destructive Metamorphism: Vapour pressure is higher above small pores  Vapour transport to the larger pores  formation of larger ice units  resulting compaction up to 1% h-1  at around 0,25 g cm-3 this effect becomes insignificant  Constructive Metamorphism (big impact) „Sintering process“: Water accumulates around the contact points of two snow flakes  Development of snow crusts  Melt – Metamorphism:  Development of snow/ ice layers Small crystals are melting at first. Remaining crystals 1-2 mm diameter  high conductivity Modelling snowmelt – approaches: 1) Energy budget 2) Temperature index approaches 3) (Heat budget) 15  Fundaments and Principles of Hydrology 1) Energy budget: physically based balances the available energy with the energy needed for the melting process  high data requirement, high measurement frequency 1a) Warming phase  Estimate the amount of energy required to raise the average temperature of the snowpack to the melting point 1b) Ripening phase  Estimate the amount of energy required to saturate the snowpack 1c) Output phase  Estimate the amount of meltwater that is produced by additional energy input Temperature index approaches  Considers only air temperature, low accuracy but easy to apply  Snowmelt is calculated as a linear function of average air temperature  Snowmelt runoff is calculated as a linear function of average air temperature ∑ meltwater = k ⋅ ∑ D [kg/m²] or [mm] 16  Fundaments and Principles of Hydrology  Temperature sum from hourly averages  Only long wave and turbulent energy input.  Melt factor k = αh ⋅ λ f [mm/degree] αh = coefficient of heat transfer: 1.. 1.5 MJ/m²/d/K λf = heat of fusion = 0.335 MJ/kg  k = 1.5.. 6 mm/degree Heat budget:  Based on temperature- humidity-wind profiles above the snow pack together with temperature measurements within and below the snow pack. Meltwater output for time steps of 6 h can be derived from tables. 7 Runoff  Is the component of the water balance that can be determined most reliably  Runoff is measured as river discharge, which  integrates the runoff of the catchment  The time series of runoff is called hydrograph  The runoff recorded at a gauging station is integrating all hydrologic processes of the contributing areas  Hydrograph analysis allows to quantify fast and slow runoff components, floods and droughts, flow duration curves and cumulative mass diagrams 7.1 Runoff measurements Importance of accurate data collection  characterisation of natural systems  hydrologic modelling  Garbage in, garbage out Measurement of hydrological data requires adequate equipment and sufficiently trained technicians Site selection: consistent (stable) relationship between stage/depth and stream flow. Reliable measurement of stage / flow.  consistent point of reference (gauge zero)  straight river section with constant slope  no obstructions, weeds, backwater, … Sampling: objective of the investigation determines the required sampling frequency:  Discrete data - single values  Continuous data - hydrograph (e.g. for flood forecasting) Measurement of river discharge  ensure a stable ratio between stage/depth and discharge and an easy measurement of flow on discharge site  goals of the investigation determine the necessary temporal/spatial resolution of the data (monthly values for the progression in one year, hourly values for flood forecasting) o Discrete data  single values o Continuous data  hydrograph 17  Fundaments and Principles of Hydrology Measurement methods 1) Measuring stage → deriving discharge 2) Measuring stream flow / velocity (directly) 1) Stage gauges stage = water level above a fixed reference point (gauge zero)  manual gauges (non-recording): most common = staff gauge → graduated plate fixed in the stream, river bank or on a structure, e.g. a bridge  mechanical float gauge recorder o continuous recording  hydrograph o transmission of stage over a float or press o option: digital data collection and remote transfer  pneumatic gauge / pressure sensor o measurement of hydraulic pressure: p = ρ ∙ g ∙ h o  continuous pressure / stage recording o remote data transfer possible o less frost susceptible compared to float gauge recorder o reliable measurements in rivers with high sediment load 2) Flow measurements → flow velocity Flow velocity is measured using current meters.  depth-velocity curves are measured at several points by counting the number of rotations of a current meter during a period of time  Other measures: weirs and flumes, tracer methods, indirect methods (slope-area), electromagnetic and acoustic (ultrasonic) flow measurements  most common method of discharge measurement is the "area-velocity-method" using the continuity equation: [m3 s-1] Stage – discharge (flow rating) curve of the river profile. This is the functional relationship between water stage and discharge  corresponding pairs of Q and h are measured to establish Q(h), (the function may change over time) stage-discharge curve:  used to determine streamflow for a given water level  relation depends on geometry and hydraulic properties of the cross-section  regular verification of Q(h) 18  Fundaments and Principles of Hydrology  flood wave propagation is a non-stationary process: for the same stage the discharge is higher at the ascending branch of the flood wave than at the descending branch   hysteresis of the stage-discharge curve Maximum flow rate occurs before the highest water level! Other methods to measure stream flow:  Weirs (height measurement)  Tracer methods o analysing break-through curve of salt or fluorescent tracer o tracer attenuation related to discharge; c ~ Q o continuous or pulse injection... Discharge in m³/s... Tracer volume in mg... Concentration in mg/time... Time in s Ultrasonic-Doppler-method:  ADCP - Acoustic Doppler Current Profiler  acoustic signal with a given frequency is emitted  signal is scattered by particulate matter and reflected  the frequency of the reflected signal is shifted depending on the flow velocity 7.2 Hydrograph analysis Hydrograph analysis  time series analysis  useful functions / characteristics for hydrological analysis: - mass curve - mean discharge - mass curve of differences to average - flood volume - flow duration curve - … 19  Fundaments and Principles of Hydrology  Mean discharge, MQ  mass curve: the time integral of the hydrograph: t SQ = ∫ Q (t )dt = ∆t ⋅ ΣQ t0  continuous slope of the mass curve: ∆t ⋅ Σ MQ  inflection points in the mass curve  local maximum / minimum of the hydrograph  mass curve of differences to average: SDQ = ∆t ⋅ (ΣQ − Σ MQ ) Application:  time dependent difference between inflow and outflow (discharge) of a river reach or reservoir  comparison of the inflow - and the discharge mass curves  storage or withdrawal within a time interval  significance for reservoir dimensions and storage simulation Flood volume  integration of the flood hydrograph from a critical flow / water level to the peak discharge QS: Qs F = ∫ Q(t ) ⋅ dt RQ  for flood protection and reservoir design Flow duration curve  a cumulative frequency curve showing the percent of time during which discharge were equalled or exceeded in a given period  the integral of the frequency diagram o Ordinate: observation value o Abscisse: duration values (abs. cum. freq.) o Duration curve, non-exceedance : DF o Duration curve, exceedance: DP o DP + DF =N o Median: DF = DP =N/2  Relevance o statistical criteria (flood re-occurrence probability, navigability of waterways) o economic criteria (e.g., power generation, water usage) o ecological criteria (e.g. minimum discharge, inundation areas)  Estimation method o sort by size o [bin (daily) discharge for a time period (year) → frequency diagram] o calculate absolute cumulative frequency = duration curve  Main assumptions: o continuous data record (bias, variance) o observed fluctuations are randomly distributed around a stable mean o annual variation and periodic processes caused by climate and catchment characteristics 7.3 Floods and Droughts Hydrological Extreme Events  Flood → river discharge rising to a multiple of the average discharge over a short period of time.  Drought → river discharge falling below a critical limit over extended periods of time. 20  Fundaments and Principles of Hydrology 7.3.1 Floods Flood: temporal limited rise of the discharge up to a multiple of the average discharge Reasons for floods  meteorological: precipitation, snow melt, ice, storm surge etc.  catastrophes: failure of dams, earth-/seaquakes Flood protection, monitoring stage/discharge hydrograph  operative flood protection  water level  maps of inundation areas, navigation, constructions in endangered areas  flood peak discharge  design, river training, relief facilities  high water duration  dike safety, flood damage  discharge sum  design of retention basins, storage reservoirs Design flood = hypothetical flood hydrograph or peak discharge, used for the design of a hydraulic structure or river control  e.g., flood with 100 year return period:  estimation of extreme events challenging  length of the discharge data record limited  sample volume!  ungauged cross-section, ungauged catchments? Estimation of design floods for short data records / ungauged cross sections:  correlation analysis o for short records, not for ungauged cross-sections o similar discharge characteristics as neighbouring gauges? o use reference gauge with longer data record to extrapolate to gauge with short discharge time series  reference HQ-method o for ungauged cross-sections o assumes similar probability (flow duration) curves in homogeneous regions o assumes a simple relation between reference flood and characteristic parameters of the catchment (e.g. area) Estimation of design floods for long data records: Statistical analysis of the hydrograph  determine maximum annual characteristics (peak discharge, flood volume) from observed or simulated time series  consistency test  empirical occurrence probability  theoretical prob. distribution  choice of the return period, T;  determine HQ (T) 7.3.2 Droughts River discharge falling below a critical limit over extended periods of time. → limit depending on water usage, ecological criteria, … Reasons  typically weather /climate Drought types  meteorological drought: extreme and prolonged deficit in precipitation, often with high temperature, solar radiation, wind, and low humidity  leads to agricultural drought: unusually low soil moisture (and no groundwater recharge)  leads to decline in stream discharge, lake, wetland, and reservoir levels, groundwater levels below a critical level: hydrological drought Characteristics  low flow, Qcrit and duration, D o e.g., 7Q10: 7-day low flow with a 10-year return period  low water level 21  Fundaments and Principles of Hydrology  deficit volume, spatial extension  frequency, re-occurrence interval  drought severity, S (cumulative deviation from critical level)  drought intensity, I (magnitude), I = S / D Indicators of low flow periods  water use restrictions Concepts for the determination of low water periods  statistical analysis (analogue to the high water): one-dimensional: NQ variable for ND = constant or ND variable for NQ = constant; two-dimensional: NQ and ND variable  regional analysis for unobserved cross sections Estimation of low flows /droughts (analogue to design floods)  Statistical analysis  basis for the design and operation of reservoirs (e.g. drinking water - , irrigation reservoirs, hydropower lakes, …) o 1-dimensional: low flow for constant duration (e.g., annual daily min flow) or duration of critical flow threshold (e.g., days below Qcrit) o 2-dimensional: low flow for variable durations  regional analysis for unobserved cross sections o (correlation analysis, reference LQ method) …  Low flow periods closely connected to soil storage and groundwater storage 7.4 Runoff components  Streamflow is a combination of base flow, interflow and saturated overland flow  Factors affecting runoff: rainfall pattern, land surface, topography, catchment shape & size, vegetation, geology, weather, antecedent soil moisture… 22  Fundaments and Principles of Hydrology 7.5 Runoff formation Which proportion from the precipitation is running off? Precipitation = net precipitation + infiltration + losses Net precipitation = overland flow + interflow Net precipitation = direct flow  different land use  different transformation of precipitation in different areas of the watershed SCS Method  developed by the Soil Conservation Service (SCS) of the United States Department of Agriculture (USDA)  based on empirical relationship between the retention and runoff: → estimation of the effective storage capacity of different soils & landuse types → estimation of infiltration for a given precipitation event → excess infiltration = runoff  developed for agricultural watersheds in the mid-western US  for small to medium sized ungauged catchments  used worldwide Continuity Equation Proportionality Infiltration excess P − Ia = F + Q + F = Q → Q= ( P − Ia ) 2 S P − Ia (P − I a ) + S with: Q = runoff P = precipitation S = maximum potential retention Ia = initial abstraction = λS (0 < λ < 0.3) F = actual Infiltration  assuming: Ia = 0.2*S removes the initial abstraction from the equation: Q= ( P − 0.2 S ) 2 (P + 0.8 S )  The potential maximum retention, S, is determined by the Curve Number (CN), 0 ≤ CN ≤ 100: 1000  100  (for S in mm) S= − 10 (S in inch) S = 254 ⋅  − 1 CN  CN   The CN for a given area is determined on the basis of landuse, landcover, soils and other criteria  CN related to antecedent moisture condition (AMC) in the catchment 23  Fundaments and Principles of Hydrology  three AMC classes, standard tables for CN II Application  adequate for ungauged catchments  easy to use, data often accessible  for middle Europe: CN-Values 10 to 30% underestimated  understimation of Peff – initial abstraction too high?  no consideration of P duration 7.6 Runoff concentration Runoff concentration: streamflow response = Water moves from the contributing areas on surface and subsurface flow paths → discharge at the outlet cross section Factors influencing runoff concentration:  non-uniform temporal distribution of catchment rainfall  spatial distribution of catchment rainfall  event track direction  location and size of urban areas  shape and structure of the catchment  stream density Estimation of runoff concentration by the hydrological system approach: Unit Hydrograph  characteristic response of a catchment to a unit volume of effective precipitation applied at a constant rate for a given time  instantaneous unit hydrograph: unit volume applied instantaneously → permits continuous math concept for transfer function  Main assumptions: o Stationarity: transfer function h(t) is time invariant o Proportionality: direct flow scales linearly with the effective precipitation o Superposition: direct flow at time t is the summation of the single outputs at t  Linear model 24  Fundaments and Principles of Hydrology  Calculation of the hydrological response function h(t) using the: convolution integral discrete convolution integral t n q (t= ) ∫ p(τ ) ⋅ h (t − τ )dτ 0 = q (tm ) ∑p i =1 m −i +1 ⋅ hi ⋅ ∆t Linear Storage Model 1 Storage: q= S S = K ⋅q K ∂S Continuity: p =q+ ∂t ∂q Differential equation for linear storage: p =q+K ∂t Analytical solution: − ( t −t0 ) t 1 − ( t −t0 ) K q (t ) = q (t0 ) ⋅ e K + ∫ p (τ ) e dτ t0 K k = storage coefficient [h]; S = storage [m³]; p(t) = inflow [m³/s]; q(t) = outflow [m³/s]  instantaneous unit impulse at time t0 = 0: S (t0 ) = 1 q (t0 ) = 1 / K  depletion of storage with no further inflows leads to the impulse response h(t) of the linear reservoir: 25  Fundaments and Principles of Hydrology 1 −t / K h(t ) = ⋅e K Linear Storage Cascade 1 −t / K  Impulse response of single reservoir: h1 (t ) = ⋅e K n −1  depletion of storage with no further inflows 1  t  → impulse response of storage cascade: hn (t ) = ⋅  ⋅ e −t / K K (n − 1)!  K   Assumption: reservoirs empty t0 = 0  n influences the shape of the hydrograph (Translation)  K determines the position of the peak discharge (Retention)  by variation of n and k processes of translation and retention can be simulated within the catchment  Estimation of n and K o directly from geomorphological characteristics o indirectly from hydrograph analysis (e.g., max. likelihood, method of moments, least square fit) 7.7 Flow routing  Wave attenuation: caused by channel geometry, resistance and retention → unsteady flow  Black‐Box: regression, statistical methods  Conceptual: linear reservoir, translation function, Muskingum method  Physically based: shallow water equations (Saint-Venant, typically 1D) Hydrodynamic approach: 1D Saint-Venant equations  unsteady flow, simplification by neglecting inertia and pressure terms 7.8 Rainfall-runoff modelling  Various model types and models are used for Rainfall‐Runoff modelling (see chapter 5.2): o Empirical models (black box) o Conceptual models (grey box) → widely used in engineering hydrology o Physically based models (white box) o Stochastic models 26  Fundaments and Principles of Hydrology  Model choice is depending on the goal of the investigations (model purpose), the watershed or model domain, characteristics and the data availability  Transformation of rainfall into runoff by various interacting processes, which are classified into three groups for the development of conceptual models: o Runoff generation o Runoff formation o Flow routing (wave propagation)  Conceptual models applied for: o (operational) flood forecasting o water balance calculations o land use / climate change impact studies o estimation of design values o …  Physically based models applied (additionally) for: o groundwater flow and surface water interactions o soil-plant-atmosphere systems o contaminant transport o hydrological change o process identification o … 8 Evapotranspiration  Link between water and heat balance  all processes by which liquid (or solid) water at the land surface becomes atmospheric water vapour  globally 62% of P on land  typically ETR > R  evapotranspiration consumes energy and cools the evaporating body  Water molecules carry energy → turbulent flux of latent heat  depends on water & energy availability, humidity gradient, wind, vegetation physiology, … Practical importance:  P – ETR = water available for direct human use  → water resources management  70-75% of ETR is transpiration by plants  → food security, efficient irrigation,  Understanding and predicting climate change  requires the ability to model ETR which is a  major component of energy and water-vapour  exchange between land and atmosphere  ETR influences yield of water-supply reservoirs  Evaporation from rivers, lakes, bare soil (ca. 10-15 % of total evapotranspiration)  Evaporation from interception by vegetative surfaces (ca. 15%)  Transpiration (ca. 70-75%)  Sublimation from ice and snow (surface and wind blow) (ca. 1-2%) 8.1 Evaporation  Occurs when water is converted into water vapour by energy transfer  Energy controlled diffusive process that follows Fick’s first law 27  Fundaments and Principles of Hydrology with: E … evaporation rate ν … wind speed a e , e … vapor pressures of the evaporating surface and the overlaying air s a K … coefficient of vertical transport efficiency E  the vapour pressure of an evaporating surface is equal to the saturation vapour pressure at the surface temperature  Potential evaporation EP [mm/day]: o volume of water evaporated from a unit area per unit time, [mm/d] o theoretical concept: free-water evaporation → dependent only on meteorological factors o most common method of measuring EP: evaporation pans (class A pan)  Actual Evaporation EA: o reduction of EP by limited water supply  Measurement and estimation of evaporation Reliable point data on actual evaporation can be obtained by: o Class A pan for open water surfaces and bare soil o Allen et al. (1998), FA56: 8.2 Transpiration  = diffusion of water vapor from the stomata to the atmosphere o uptake of soil water by plant roots o translocation of water through vascular system o evaporation through stomata  not a metabolic process!  driven by available energy and potential gradient e.g., Ψsoil -0,1 MPa > Ψroot -0,5 MPa > Ψleaf -2 MPa > Ψair -30 MPa 8.3 Interception Is the temporary storage of precipitation at the surface of plants – subjected to evaporation. Main processes: o R … total rainfall o Rt … throughfall o Rs … stemflow o Ec … canopy interception loss o El … litter interception loss o Rn … net rainfall 28  Fundaments and Principles of Hydrology interception loss depending on:  storage capacity of plant cover: o vegetation type, o development stage o → LAI  Precipitation characteristics: o intensity o duration o frequency  Evaporation rate → direct measurement difficult Modelling approaches  Rutter model (Valente et al. 1997)  Simpler approaches based on interception storage capacity  −P  I = SI max 1 − e SI max  + k ⋅ P   with: I … interception [mm] SI … capacity of interception storage [mm] max P … total precipitation k … constant, f (LAI, I, duration) EI … = k*P, evaporation from interception 29  Fundaments and Principles of Hydrology 8.4 Evapotranspiration - measurement and estimation  Potential evapotranspiration, PET o = max. ET rate from an uniform vegetation cover with unlimited water supply (& no advection, no heat storage)  Reference evapotranspiration, ET0 o Penman (1956): “.. the amount of water transpired by a short green crop, completely shading the ground , of uniform height, and never short of water”  Actual evapotranspiration, ETR o = limited water supply reduces PET to ETR Methods for estimating potential evapotranspiration, PET  Pan, (corrected) free-water evaporation:  temperature-based, e.g. Thornthwaite (1948), Hamon (1963)  radiation-based (e.g. Priestley & Taylor, 1972)  combination, e.g. Penman equation for free-water surface: Penman equation ∆ ⋅ ( K − L) + ρ a ⋅ ca ⋅ (esat − e) / ra PET = ρ w ⋅ λv ⋅ (∆ − γ ) Methods for estimating actual evapotranspiration, ETR  Land surface water balance: ETR = P – R for long-term averages; estimate of ETR is too low if systematic error of P data is not corrected!  Micrometeorological methods o e.g., Penman-Montheith eq. o reference evapotranspiration  soil water balance method  Measurement of plant transpiration  Lysimeters  Turbulent mass / energy transfer methods o eddy-covariance method Penman-Monteith equation: ∆ ⋅ ( K − L) + ρ a ⋅ ca ⋅ (esat − e) / ra ETR = ρ w ⋅ λv ⋅ [∆ + γ (1 + rs / ra )] rs … stomata (canopy) resistance [s m−1], = f (LAI) well-watered Bermuda grass (12 cm high): rs = 70 s m−1, ra = 208/uz s m−1, albedo = 0.23 900 0.408∆ ⋅ ( K − L) + γ u z ⋅ (esat − e) ET0 = T + 273 ∆ + γ (1 + 0.34u z ) 30  Fundaments and Principles of Hydrology ET0 – (grass) reference evapotranspiration → most common and widely used ETR = K c ⋅ ET0 Kc = crop specific coefficient ETR from soil water balance:  measurement of ψ and θ  change of θ only by infiltration & water movement or ET (E & root uptake)  location of the zero-flux plane is shifting over time adapted from Dingman (2005) Plant transpiration  Leaf porometer  Potometer Lysimeters ETR = P - D - ∆S P … net precipitation D... drainage water ∆S... storage change eddy-covariance measurements  direct measurement, but expensive  measurement errors up to 20% (energy gap) ρa ' ' ETR = ⋅ ua ⋅ q ρw 31  Fundaments and Principles of Hydrology 9 Regional Aspects of Hydrology Hydro-climatic classification  Precipitation regime  Temperature regime  ET / EP ratio  aridity index: r > 0.5 … humid 0.5 < r < 2 … temperate r 1a  semiarid : sufficient precipitation for the seasonal agriculture Classification Aridity Index, r Global land area Hyperarid r < 0.05 7.5% Arid 0.05 < r < 0.20 12.1% Semi-arid 0.20 < r < 0.50 17.7% Dry subhumid 0.50 < r < 0.65 9.9% Global distribution of arid areas  North-Middle-Africa-Eurasia = biggest arid aria North America: arid-semiarid areas in Mexico, Great Plains South America: arid-semiarid areas mainly in the East and the South (Patagonia, Atacama desert); dry plains of central Australia occupy a large part of the continent Precipitation characteristics  high annual variability, e.g. Alice Springs mean = 286 mm; 2001: 741 mm; 2002: 198 mm  during the “wet” season cyclonal, less intensive precipitation of several days’ duration  during dry periods: convective precipitation of high intensity and short duration  distinct long-term fluctuations, e.g. 10-year average fluctuation in Mexico: 440 mm & 850 mm Evaporation  mainly from bare soil or rock, ~ 3000 mm/a  ~ 50 % of annual P (scarce plant cover)  short periods of P: no groundwater-recharge 32  Fundaments and Principles of Hydrology Surface runoff  as result of rainstorms only  little natural retention  mainly depending on slope  infiltration of fundamental importance:  ephemeral streams  gw recharge Groundwater  most important water reservoir, protected against the evaporation Irrigation  agriculture is only possible under irrigation  water quantity and quality problems Problems of salinization Soil salinization as a consequence of  high groundwater levels (over-irrigation)  saline irrigation water  increasing salinization of coastal aquifers due to excessive water abstraction  lack of leaching Aral Sea 1960 – 2003  Kazakhstan & Uzbekistan  formerly 3rd largest fresh-water lake (68000 km²)  Amu Daya (2500 m³/s), Syr Daya (1200 m³/s)  irrigation canals (cotton)  since 1960 sea water surface shrank by 70%, volume by 88%  Consequences: o economy (fishery) o ecology: death saline lake with salinity of 8% (sea water 3.5%) o health 9.2 Humid Tropics Global distribution of humid tropics  Located between the 23°30’ northern and 23°30’ southern latitude  Indonesian Archipelago  South – and Latin America  relatively small areas in Africa General characteristics:  mean P ≥ PET  humid month: P > 100 mm  three climatic subtypes: o humid: 9.5 – 12 humid months o sub – humid: 7 – 9.5 humid months o wet – dry: 4.5 – 7 humid months  low spatial variability of P  high periodicity Criteria:  mean T of at least 8 months: ≥ 20 °C  mean T of the coldest month: > 18 °C  mean air humidity of at least 6 months: ≥ 65 % Vegetation types:  tropical rain forest (humid)  monsoon rain forests (sub-humid)  savanna (wet-dry climate) Precipitation characteristics  tropic circulation  cyclonic / convective / orographic precipitation 33  Fundaments and Principles of Hydrology  rainy season / drought periods due to the distance to the equator  weather highly periodic Weather phenomena of humid tropics  daily convection (meso-scale convergence zones)  eastern disturbance (tropic Atlantic Ocean) : May-October every 3-5d periodic fluctuations of the eastern trade winds  cyclones: average precipitation of a cyclone: ~1000 mm/d  oscillation of zonal winds within a period of 30 –60 days: eastwards parallel to the equator  monsoon with the annual cycle  quasi bi-annual oscillation: strong – weak monsoon  El Nino  Greenhouse effect Evaporation  mean annual ETR ~ 1400+ mm  ETR limited by energy input  ETR / PET = 0.9... 1.0 (sufficient water supply)  deforestation:  increasing percentage of ETR from soils and low vegetation  less interception  increasing runoff Surface runoff  saturation of natural retention capacity (interception-/soil storage) runoff formation Types of flow regimes in the tropics  equatorial rivers: one seasonal peak due to high annual precipitation without a pronounced dry season  equatorial rivers: two peaks (precipitation usually over 1,750 mm/a, and basins generally covered with equatorial forests)  rivers of wet and dry tropical low lands: regions of moist savanna, highly seasonal rainfall (dry season lasting for at least three months)  rivers of wet and dry tropical highlands: moist type from woodland and savanna basins, highly variable dry season and annual precipitation  rivers of tropical mountains: influenced by altitude, slope exposure and deviation in rainfall regime 9.3 Polar regions  Arctic: Northern hemisphere, polar regions of the continents  Antarctic: Southern hemisphere, ≥ 60° Southern latitude General characteristics  high angle of incidence  energy flux is spread over a larger area  high snow albedo Mass balance:  precipitation = (mainly) snow input that accumulates  ablation  total loss of water = snowmelt + sublimation + evaporation snow melt consumes energy Precipitation characteristic  high variability + characteristic annual curve  main form of precipitation: snow  accumulation = snow deposition  rainfall limited to few locations (summer months)  increase latitude  decrease rainfall 34  Fundaments and Principles of Hydrology  in the centre of the polar regions exclusively snow precipitation (missing inflow of mild air masses)  low saturation vapour pressure of the cold air  precipitation of low intensity  determination of the precipitation: snow gauge measurements + energy balance (sublimation / evaporation) + snow deposition Evaporation  ETR = evaporation from snow covered areas  summer months: ≤ 45 % of the precipitation volume evaporates  decline of the annual evaporation with growing distance to the coast  winter months: ETR is ~ 0 Surface runoff  variability of time, duration and quantity determined by glacial melting  climate (T, Rn, snow-coverage)  glacier location (incline, altitude, exposure, albedo)  Summer: T > 0°C,  melt-water  ephemeral streams Glacier hydrology  mass balance twice a year (∆S for winter & summer)  ∆S = P - melt - sublimation  mass loss 40 – 90% sublimation;  energy balance estimation  melting = f (T, Rn, a,..)  snow depositions on glacial ice  increase in albedo  decrease in absorbed energy  decrease in melt Soil - Permafrost  high temporal and spatial heterogeneity  little soil development, coarse texture  world-wide the lowest organic carbon content / biological activity  infiltration primarily depending on the effective porosity, less on the soil temperature 35