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ESM 203: Land-atmosphere interactions

ESM 203: Land-atmosphere interactions: Water and energy balance of a vegetated soil

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ESM 203: Land-atmosphere interactions

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    1. 1 ESM 203: Land-atmosphere interactions: Water and energy balance of a vegetated soil Jeff Dozier & Tom Dunne Fall 2007

    2. 2

    3. Water and energy balance of a vegetated, soil-covered land surface For some ?t (e.g day or month) on a unit area of land, the mass balance equation for water is SM is the water content of the soil Units are [m3/(m2xt)] or depth/time (e.g., m/mo)

    4. 4 Suppose …. We can measure or predict P (depth or volume/area per time) We can predict QuickFlow (e.g. as a fraction of P) We can predict E (depth or volume/area per time) Rainfall that does not run away quickly over or under the surface, and is not immediately evaporated enters the soil.

    5. 5 And then suppose …. The soil has a fixed maximum water holding capacity: where D is the rooting zone depth (m) and ?fc is the “field capacity” of the soil (m3/m3), and depends on soil texture Thus, SMmax has dimensions of m (m3/m2 of land surface)

    6. 6 Water and energy balance of a vegetated, soil-covered land surface For some ?t (e.g day or month) on a unit area of land, the mass balance equation for water is SM is the water content of the soil Units are [m3/(m2xt)] or depth/time (e.g., m/mo)

    7. 7 And that …. Soil moisture content, SM (m3/m2), varies each day as a result of the accounting: If SM rises to SMmax, “excess” water draining from the soil recharges the ground water store, which has a volume per unit area (i.e. a depth), V that also changes each day

    8. 8 We need three values for this accounting: The water-holding capacity (field capacity) of the soil profile, ?fc The root zone depth (D) for SMmax = D x ?fc The evapotranspiration rate, E

    9. 9 Soil particles and soil pores Soils consist of particles with a range of size from clay to gravel Between the particles are irregular-shaped conduits called pores The diameter of the pores is roughly proportional to the sizes of the particles (pores in sand > pores in silt)

    10. 10 Water-holding capacity of soil or sponge Soil contains pores of differing sizes (cm to µm)

    11. 11 Experiment in the bathtub to understand the water-holding capacity of a soil

    12. 12 Experiment in the bathtub to understand the water-holding capacity of a soil

    13. 13 Experiment in the bathtub to understand the water-holding capacity of a soil

    14. 14 Experiment in the bathtub to understand the water-holding capacity of a soil

    15. 15 Water-holding capacity of soil or sponge Soil contains pores of differing sizes (cm to µm) As in a sponge, each soil pore draws in water as if it were a capillary tube

    16. 16 Water is drawn into narrow spaces by the ‘capillary’ force The capillary force arises because of the presence of curved air-water interfaces (menisci) inside the tubes The capillary force (suction) is greater in narrower tubes, narrower pores, and the narrower parts of pores

    17. 17 Water-holding capacity of soil or sponge Soil contains pores of differing sizes (cm to µm) As in a sponge, each soil pore draws in water as if it were a capillary tube The suction (negative pressure) holding water in a pore is inversely proportional to the pore diameter

    18. 18 Water in soil pores

    19. Soil water content and suction As soil dries, the menisci retreat into narrower parts of pores the suction on the remaining water in the necks of pores increases as their radii decrease As soil becomes wetter, larger pores fill and the suction in them decreases

    20. When all pores are filled (saturation) there are no air-water interfaces, so the suction is zero When the suction increases to 0.1-0.3 atmospheres, free drainage under gravity almost ceases (“field capacity”, ?fc) --- for entry into SMmax When the suction increases to about 15 atmospheres, plants can no longer extract water from the soil (“wilting point”) Soil water content and suction

    21. Soil texture affects water holding capacity

    22. So we could compute all the components of the water budget of the surface, soil, and ground water For some ?t (e.g day, or month) on a unit area of land, the mass balance equation for water is SM is the water content of the “underground store” (soil or ground water) Units are [m3 /(m2xt)] or depth/time (e.g., m/mo)

    23. We still need to evaluate evapotranspiration (E) If we could evaluate E we could use the continuity equation as an accounting procedure to calculate runoff and soil moisture for any time period We could account for the land-atmosphere interaction, including any factor such as vegetation type that might affect it E is extremely difficult to measure directly for long periods, so we usually estimate it from the energy balance (rate of expenditure of latent heat) Phase change to vapor requires an input of 2.5×106 J/kg

    24. 24 The energy balance equation (flux per unit area, W m–2) applied to a surface S = solar radiation a = albedo: water 0.06; conifer forest 0.09; Amazon broadleaf forest 0.12; grassland 0.2–0.4; snow 0.6–0.8 F?= downward infrared radiation, depends on temperature, water vapor, and clouds Ts = surface temperature H = sensible heat transfer (+ is surface to atmosphere) L = latent heat transfer in water evaporating or condensing (+ is evapotranspiration, – is condensation) G = heat conducted into soil es = surface emissivity s = Stefan-Boltzmann constant = 5.67×10–8Wm–2K–1

    25. 25 Convert latent heat flux into mass flux of water L = latent heat flux E = evapotranspiration rate (m s–1) ?w = density of water (1000 kg m–3) ?v = latent heat of vaporization (2.5?106 J kg–1) Latent heat exchange per unit area converts a volume of water (per unit area) to vapor The energy required for this conversion is the volume of water per unit area (E) multiplied by the latent heat of vaporization energy required to convert a kg of water to vapor and by the density of water which converts the mass per unit area to a volume per unit area

    26. 26 End-member situations (for day or month, G=0) Rnet = H + L Waterless planet or mid-Sahara L = 0, Rnet = H Mid-ocean or mid-Congo H = 0, (wind and underlying water have come into thermal equilibrium) Rnet = L Most places are intermediate:

    27. 27 MODIS Maximum Land Surface Temperatures

    28. 28 More general basic principle Net radiation (Rnet) drives the sum of sensible (H) and latent (L) heat exchange with the atmosphere and heat flow into or out soil (G) G is normally small Temperature, vapor pressure, and soil moisture determine how Rnet is partitioned between H and L, depending on the magnitude of the temperature gradient vs. the vapor pressure gradient above the surface the rate at which the atmosphere in the boundary layer mixes

    29. 29 Estimation of each energy component Soil heat flow (G)

    30. 30 Estimation of energy components, cont. Sensible heat flow (H) is a diffusive process driven by turbulence (eddies) in the wind

    31. 31 Estimation of energy components, cont. Latent heat flux (L)

    32. 32 Estimation of energy components, cont. Instead of using a diffusivity, K, (a measure of how easily heat or water vapor are transported away from the surface We can use the inverse of diffusivity, which is the resistance to transport, ra.

    33. 33 Estimation of sensible heat transfer from surface Ts – Ta = ?T is the difference between the surface temperature and air temperature ra is the aerodynamic resistance of the surface Depends on wind speed, roughness, atmospheric stability

    34. 34 Estimation of latent heat transfer from surface (i.e. evaporation/evapotranspiration) e*(Ts)-ea) = difference between saturation vapor pressure of a surface at Ts and the vapor pressure of the air. P = atmospheric pressure ra = aerodynamic resistance over the surface Depends on wind speed, roughness, atmospheric stability rc = resistance to vapor movement from within the stomates of canopy leaves

    35. 35 Extreme cases (for day or month, G=0)

    36. 36 Penman (1948)

    37. 37 Saturation vapor pressure

    38. 38 Potential evapotranspiration Equations like Penman’s ‘assume’ that the vegetated surface (i.e. inside of the leaf stomates, the soil and water bodies) is wet enough to be freely evaporating without biotically imposed restriction (such as partially closed stomates) We call E computed for this condition the Potential Evapotranspiration (PE)

    39. 39 Converting Potential Evapotranspiration to Actual Evapotranspiration

    40. 40 Soil texture affects water-holding capacity Difference between field capacity and wilting point is the “available water- holding capacity” (AWC)

    41. 41 Conversion from PE to AE The shape of the function f depends on the soil texture

    42. 42 Monteith (1965) Monteith (1965) – brought plant physiology into the land- atmosphere interaction model by including a “canopy conductance” term, Kcan This new conductance represents the ease with which water vapor can escape from leaf stomates and all the leaves in the canopy. Thus, he altered Penman’s equation to :

    43. 43 Penman-Monteith equation (7-56 in Dingman) for potential evapotranspiration Java code to calculate this is available at http://www.ierm.ed.ac.uk/cw2h/lec8/pm10.htm

    44. 44

    45. 45 The variables …

    46. 46 Penman-Monteith Equation parameters KL or ra represent the conductance from the surface into the atmosphere, and depends on surface roughness and the stability of the atmosphere Kcan or rc represents the conductance out of the stomates and canopy into the atmosphere As Kcan ? 8 {or as rc ?0), the Penman-Monteith equation becomes the original Penman equation -- i.e. as the canopy becomes “infinitely conductive”, or as it provides no canopy resistance to vapor escape to the atmosphere, and E? PE. For example, water on the surface of leaves during and after rain. Kcan decreases from leaf surface to leaf stomate, and as the soil becomes drier and the soil must exert greater suction to draw water from the soil pores.

    47. 47 Penman and Monteith Penman E = s RN + ? KL ?w ?v u [es(Ta)-ea] ?w ?v [s + ?] Monteith E = s RN + ? KL ?w ?v u [es(Ta)-ea] ?w ?v [s + ?(1+KL)] Kcan

    48. 48 Controls on canopy resistance LAI is the leaf area index of a vegetation cover (m2/m2) 1 grassland 5 deciduous hardwoods in growing season 10 tropical rainforest 10-50 temperate coniferous rainforest Kleaf = f(species, [es-ea], Ta, SM) The coefficient for species has a range of at least a factor of 2

    49. 49 Biotic controls on evapotranspiration Note where vegetation characteristics enter the energy and water balance Rnet contains (1-a) ra contains surface roughness, proportional to height rc contains species, LAI, and the depth of the rooting zone

    50. 50 Runoff in the water balance ?=volume fraction of water V(t)= volume of groundwater storage resulting from balance between drainage from soil and drainage to rivers Q(t) D=depth of root zone

    51. An example of vegetation change affecting water supply (Eschner and Satterlund, 1966, Water Resources Res.)

    52. Resulting in a decrease in dormant season runoff, because of increased interception and evaporation of rain and snow, especially under conifers

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