Water balance in soil

Transcription

1 Technische Universität München Water balance Water balance in soil Arno Rein Infiltration = + precipitation P evapotranspiration ET surface runoff Summer course Modeling of Plant Uptake, DTU Wednesday, 19 June 2013 HEAT FLUXES! Heat as the driving force temperature T Hydrological cycle TRANSPIRATION Chow et al 1988, Precipitation Evaporation Transpiration Infiltration Water balance and mass transport AIR PLANT SOIL WATER GW MASS (*) system USGS (wwwrcamnl.wr.usgs.gov) Dry & wet deposition Volatilization, Plant uptake & phytovolatilization Leaching to GW Stomata (*) e.g. particles, nutrients, contaminants 10-30μm in length, /mm2 of leaf, 0.3-1% of leaf area Primary purpose: CO2 uptake. Transpiration is an unavoidable water loss 1

2 Plant growth and transpiration Transpiration is linked to plant growth Many annual crops show a logistic growth curve (known from agricultural production): initial growth is exponential towards ripening, growth slows down and finally stops Change of plant mass M [kg]: dm k M dt Evapotranspiration LAND SURFACE PROCESSES dm dt M k M 1 M max k First-order rate constant [1/d] (for exponential growth) M max Maximum plant mass [kg] Plant mass as a function of time, with M(t=0) = M 0 : Mmax M t M max 1 1 e M 0 k M 0 Initial plant mass [kg] t Chow et al 1988, Plant growth and transpiration Plant growth induces transpiration: Evapotranspiration LAND SURFACE PROCESSES dm M Q T C TC k M 1 dt M Possible scenario, annual seed plant: max Q Transpiration [L/d] T C Transpiration coefficient [L/kg dw] Typical range of T C in humid areas: 300 to 650 L transpired water per kg produced biomass (dry weight) assumption: transpiration takes place only when plant is growing strongly simplified! without consideration of e.g. solar energy influx, water and nutrient supply Evaporation process from the liquid phase as the loss rate from a surface Estimate of evapotranspiration: given as equivalent depth of water lost over a selected time period In energy terms this can also be expressed as a flux of latent heat Thus: evaluation of evapotranspiration into gaseous phase, considering gain of water vapor by the air (absorption of water vapor by air is measured over time) To complete energy balance, estimation of the fluxes of sensible heat is also important Definitions LAND SURFACE PROCESSES Evaporation: Water taken up by the atmosphere from wet surfaces ( drying ) Transpiration: Water loss from plants to the atmosphere through their stomata Evapotranspiration: The sum of evaporation and transpiration Potential Evapotranspiration: Evapotranspiration from a wet surface (water availability is not limiting the ET) Reference Evapotranspiration: Evapotranspiration from a defined reference surface Actual Evapotranspiration: Evapotranspiration from an arbitrary surface in arbitrary wetness conditions 2

3 Land surface fluxes Equivalence of volumetric and energy units of ET A volumetric water flux (Evapotranspiration) can always be expressed as an energy flux (latent heat), since a fixed amount of energy per unit of water is used to convert the water from the liquid phase to the gas phase EVAPORATION: water from aqueous phase into liquid phase This phase shift needs energy, this is stored as LATENT HEAT in water vapor exchange through land surface (LS) of: (function of wind speed) Assumption: Zero storage capacity of the LS for water, momentum and energy, i.e. instantaneous balance of all fluxes Latent heat flux [W/m 2 ] ( = J/s /m 2 ) λ Evaporation [m 3 /m 2 /s] = [m/s] ET: our unknown! work & power, units: Energy, work, heat: in [J] = [N*m] = [kg *m/s 2 * m] Power, heat flux: work per time, in [W] = [J * s] = [kg *m/s 2 *m /s] Land surface water fluxes P ET Land surface energy fluxes Rn λet I G Precipitation P, in [m 3 /m 2 /s] = [m/s] Infiltration I, in [m 3 /m 2 /s] = [m/s] Evapotranspiration ET, in [m 3 /m 2 /s] = [m/s] ET: our unknown! Surface energy balance: units [W/m 2 ] Sensible heat flux ( actual heat flux in soil) λ Net radiation (*) ( input from the sun ) Ground heat flux (convection of heat to ground) Latent heat flux (associated to vaporization of water) (*) Rn: Short-wave and long-wave radiation S and L [W/m 2 ] Equivalence of volumetric and energy units of ET A volumetric water flux (Evapotranspiration) can always be expressed as an energy flux (latent heat), since a fixed amount of energy per unit of water is used to convert the water from the liquid phase to the gas phase EVAPORATION: water from aqueous phase into liquid phase This phase shift needs energy, this is stored as LATENT HEAT in water vapor from before, rearranged: Net radiation Surface energy balance λ 0 Latent heat flux Convection of heat to ground Sensible heat flux W : density of water Latent heat flux [W/m 2 ] (we can relate to this from measurements) λ L e : latent heat of vaporization of water Evaporation [m 3 /m 2 /s] = [m/s] ET: our unknown! 3

4 Land surface momentum fluxes Vapor saturation pressure curve Vapor pressure deficit = e * (T) e(t) e*(t) or e S (T): saturation water vapor pressure at temp. T e(t) or e a (T) = actual vapor pressure at T (from before) Momentum flux (-) due to wind shear in units of [kg m/s m -2 s -1 ] = [kg/m/s 2 ]. This is absorbed by the friction force () at the land surface. unit [hpa] = 100 Pa; with T in [ C].. or: unit [Pa]; with T in [K] slope of the saturation pressure curve: with T in [K] e s e a ABOVE CURVE: air saturated with water vapour BELOW CURVE: under-saturated with water vapour T d = dew point temp at vapour pressure e a = temperature at which air mass with vapour pressure e a becomes saturated T d T Quantifying Evapotranspiration using Haude s method Derivation of the Penman equation Empirical calculation of monthly sums of potential evapotranspiration Or: Culture colza, rape rye winter wheat summer barley grass maize sugar beet, empirical Haude factor (= monthly plant factor) saturation deficiency of water vapor in air [hpa], p 14: Air saturation vapor pressure at day time 2 pm [hpa] unit [mm/d] e S: air saturation vapor pressure e: air vapor pressure φ 14: relative moisture of air at 2 pm [%] temperature T [units of C] (T at day time 2 pm used here) [1 hpa = 100 Pa = 1 mbar (10-3 bar)] a Haude, tabulated values e.g. for different crops in Germany Penman s fundamental trick: Linearization of the relationship between saturation water vapor pressure and temperature. Saturation vapor pressure (kpa) T 2 T s Air temperature ( C) This approximation works well if T 0 and T 2 are not too different. Quantifying Evapotranspiration using Haude s method Penman s empirical relationship for open water Empirical calculation of monthly sums of potential evapotranspiration Or:, empirical Haude factor (= monthly plant factor) saturation deficiency of water vapor in air [hpa], p 14: Air saturation vapor pressure at day time 2 pm [hpa] unit [mm/d] e S: air saturation vapor pressure e: air vapor pressure φ 14: relative moisture of air at 2 pm [%] temperature T [units of C] (T at day time 2 pm used here) [1 hpa = 100 Pa = 1 mbar (10-3 bar)] a Haude, tabulated values e.g. for different crops in Germany Culture colza, rape rye to estimate ET,pot with Haude we only need: easily done estimation; winter wheat -) measured temperature disadvantage: only ROUGH ESTIMATE! summer barley grass -) measured relative moisture (among others, low time resolution maize -) the vegetation cover and respective Haude factor sugar beet 1 Data requirements: Radiation Ground heat flux Air temperature at 2 m height Air relative humidity at 2 m height Wind speed at 2 m height Derived from surface energy balance λ 0 Net Latent radiation heat flux Convection of heat to ground Sensible heat flux 4

5 Example: evaporation from open water, observed vs. estimated with Penman Accuracy of the approach Actual ET, Penman-Monteith Evapotranspiration only takes place if the water content in soil is sufficiently high, = actual ET Assumption: if water content > permanent wilting point PWP Field capacity Moisture content fc at which water will no longer drain under gravity (saturated soil reaches field capacity within a few days) FC Wilting point Moisture content wp at which plants can no longer draw water from the soil PWP Wind speed Wind direction Actual ET, Penman-Monteith Incoming shortwave radiation Solar panel Evapotranspiration only takes place if the water content in soil is sufficiently high, = actual ET Assumption: if water content > permanent wilting point PWP Potential ET, = reference ET Rain gauge Temperature Rain & humidity gauge Datalogger enclosure Legind et al K C,Ini is the crop coefficient from the initial growth stage of the crop (value of 0.3 used as best estimate for cereal crops) used in the Buckets model approach as loss process from surface (besides run-off), let s look at an example Penman-Monteith Equation, Potential ET from before, OPEN WATER: 1 at VEGETATED SURFACE (implemented in Bucket Model, Legind et al. 2012) Modeling example 1 λ 1 G: soil heat flux [J/s/m 2 ] R n: net solar radiation [J/s/m 2 ] : psychrometric constant [kpa/ C] a is the mean air density at constant pressure [kg/m 3 ] c p is the specific heat of the air [J/kg/ C] : latent heat flux [J/kg] r a : atmospheric resistance [s/m], (resistance from the vegetation upward, involves friction from air flowing over vegetative surfaces, roughness length) r a = 208 / u 2m (with u 2m wind speed at 2 m height) r s : (bulk) surface resistance [s/m] e: actual vapor pressure e*: saturation vap. pr (unit [kpa]; with Ta in [ C]) : slope of sat. water-vap. pr. curve Potential ET is different for different vegetation type; r a and r s both depend on crop type! r s : complex function of different variables, most important vegetation type & soil moisture; r s is 70 s/m for surface resistance of short grass, r s = 200 / LAI (LAI: leaf area index) TRANSPIRATION RATE Q ACTUAL TRANSPIRATION Did consider water loss by plants DOUBLE, i.e. with Q and with ETactual?? NO: it is controlled by the available water content in the top layer, taken up by the CROPS in summer, and be weeds in autumn/spring 5

6 Water balance methods Lake evaporation Small scale: Lysimeters Large scale: Catchment water balance S P: Precipitation Q 0 : Superficial runoff Q GW : Subsurface runoff S: Change in storage (can be assumed close to 0 for long time intervals) Typical pan coefficient for annual lake evaporation ~0.7 Pan Coefficient: The ratio of the amount of evaporation from a large body of water to that measured in an evaporation pan Why is lake evaporation less than that recorded by pan? Seasonal variation Pan evaporation The most widely used method to estimate evaporation Class 'A' Pan The U.S. Weather Bureau Class A Evaporation Pan is 1.2 m in diameter and 250 mm deep. When installed it is elevated 150 mm off the ground. The operating water level is a depth of mm. The water level in the pan is therefore kept mm from the rim. A stilling well located on the side of the Class A Pan has a level sensor and is used to record the water depth. The measurements can be taken automatically. Note: Changed pan size can change measurement by up to 30%! Average = 0.71 Lake Hefner (USA) data Peter Bauer-Gottwein, DTU V Pan evaporation E P H 1 H 2 pan coefficient mainly depends on wind speed and relative humidity If wind speed and/or RH are low: contact layer gets saturated rather quickly, therefore less E compared to pan Variation of pan coefficient with wind Evapotranspiration Pan coefficient Pan evaporation Shaw,