BEE 6740 Spring Ecohydrology. w = density of water [10 3 kg m -3 ] T = temperature [ o K or o C]

Transcription

1 BEE 670 Spring 00 Ecohydrology Daily Epotranspiration via Penman-Montheith Notation: ET = Epotranspiration = Q e /( v w ) [m d - ] v = latent heat of porization [500 kj kg - ] w = density of water [0 3 kg m -3 ] T = temperature [ o K or o C] v = por density [kg/m 3 ] o v = saturation por density [kg/m 3 ] e = por pressure =.6x0-6 v T [mb] {T in o K} Penman-Monteith Equation (Monteith, J.L Eporation and environment. In: Proc. 9 th Symposium Soc. Exp. Bio. P ) () Q e Q o Ca ra r c ra rn [kj m - d - ] o vs = saturated por canopy surface [kg m -3 ] = por density of air [kg m -3 ] ~ psychrometric constant [.95x0 - kg m -3 o C - ] = C v = slope of the saturation curve on the psychrometric chart [kg m -3 o C - ] x0 exp T for 0<T<5 o C [kg m -3 o C - ] 3.05x0 exp 0. 06T for T<0 o C [kg m -3 o C - ] r a = atmospheric resistance to por transfer, very sensitive to windspeed [d/m] z d zh z d z ln ln z h zm () r a = uk m ln ~ z m uk X 8600 s/d u = average windspeed [m/s] k = von Karman Constant [0.] z = measurement height [m] z m = momentum roughness parameter h [m] z h = heat roughness parameter 0.z m [m] d = zero plane displacement ~ 0.77h [m] h = vegetation height [m] NOTE: because the sensitivity of Eq. () to wind, the Penman-Monteith equation is often implemented over short time-steps (minutes to hours) and summed to get a total for a day.

2 BEE 670 Spring 00 r c = canopy resistance to por transfer, very sensitive to windspeed [time m - ] rleaf (3) r c = f LAI sh f sh = fractions of canopy in shade, sparse veg. =, full canapy = [-] LAI = leaf area index, leaf area per unit area of ground [m m - ] Leaf Resistance (most of this originates with Jarvis 976) Basic concept, minimum leaf resistance (species specific) is scaled by unitless factors (f) to account for stomatal resistance incurred due to rious environmental characteristics: rmin () rleaf [time m - ] f f f f f S T other r min = Minimum leaf resistance (see table below) [time m - ] f S = dependence on solar radiation [-].78Sin (5) = [from Stewart 988 via Dingman 00].57S 0. in S in = incoming solar radiation [KJ m - d - ] f T = dependence on air temperature (there are relationships for soil temp too) [-] 0 T 0.8 a Ta 0 Ta (6) = 0 Ta 0 [from Stewart 988 via Dingman 00] 69 0 Ta 0 (7) = 0.08 a 0.006T a T [Dickinson et al. 99 via Wigmosta et al. 99] T a = air temperature [ o C] f = dependence on the por pressure deficit [-] (8) = [from Stewart 988 via Dingman 00] = por density deficit (sat. por desnity air por density: o - ) [kg m -3 ]

3 BEE 670 Spring 00 f = dependence on soil moisture (there are relationships for soil tension too) [-] 0 (9) = Ta fc [from Feddes et al. 978 via Wigmosta et al. 99] fc 0 fc = volumetric soil water content [m 3 m -3 ] Alternatively, - =ailable water and fc - =ailable water capacity NOTE: wilting point () and field capacity (fc) are convenient thresholds to approximate when stomates are fully closed and open, respectively, but may be plant specific. F other = dependence on other factors, eg. Carbon dioxide [-] Table. Some vegetation/land cover parameters adopted from the Community Climate Model (CCM)*: Albedo Max LAI Min LAI r min [s m - ] Crop/mixed farming Short grass Evergreen (needle) Deciduous (needle) Deciduous (leaf) Evergreen (leaf) Tall grass Desert Tundra Irrigated crop Semi-desert Ice Wetland Fresh water Ocean Evergreen (shrub) Deciduous (shrub) Mixed woodland *Dickinson, R.E., A. Henderson-Sellers, P.J. Kennedy Biosphere-atmosphere transfer scheme (BATS) version e as coupled to the NCAR Community Climate Model. NCAR Technical Note NCAR/TN-387+STR 3

4 BEE 670 Spring 00 Leaf Area Index: There are two primary modeling strategies (i.e., not using some kind of measurement) based on fixed time or thermal time, but, both have similar functional shapes (see figure below). Ep. efficiency, k e LAI Root-depth, Z r max Dormant Early growth Rapid growth Full grown Begin senescence Dormant min 3 5 time Although here we are interested in the LAI, similar modeling approaches could be adopted to account for root depth, i.e., soil depth from which plants uptake water, which affects the AWC, or a general eporation efficiency, which can be used to scale PET to account for plant development. The primary issue here is to estimate LAI for Eq. (3). Stewart et al. (988) used the following time-based estimates for Thetford Forest in the UK: (0) LAI = J /00 0 J 5..86J /00 5 J J /00 5 J J /00 3 J J /00 37 J 365 [based on Beadle et al. 98] Obviously, this approach is going to be somewhat different from location to location. J = Julian day or day of the year [day]

5 BEE 670 Spring 00 We developed a thermal time LAI model that was developed for the Soil Moisture Routing Model (SMR aka SMDR) (e.g., Frankenberger et al. 999, Easton et al. 007) based loosely on data from Goudriann and n Laar (99). Thermal time for day t is: Ta Tb Ta Tb () D t = 0 Ta Tb Thermal time is kept by accumulating degree-days of daily thermal time, DD. The numbered threshold points in the plant development in the figure above are determined based on accumulated thermal time. Growth begins (): In temperate areas, it is common to assume growth starts when the average five-day temperature is above the base temperature (see table ). Table outlines degree-day thresholds in percent of maximum cumulative heat units (a.k.a. potential heat units) for different vegetation/land covers. Table. Base temperature, key threshold thermal-times (% of maximum cumulative heat units) corresponding the figure above, and maximum cumulative heat units for rious vegetation/land cover types. Deciduous forest / mixed forest /shrubland Base temp. T b ( o C) Rapid growth (%) Full growth 3 (%) Begin Senescence (%) Maximum cumulative heat units (deg-days) Evergreen forest Natural grasslands Hay / fallow /pastures Row crops / small grains Recreational grasses [-] Dormancy (5): Dormancy can be initiated in a riety of ways, including, crop harvest, frost, or a maximum cumulative heat units. One approximation for (killing) frost conditions is when the mean five-day temperature is lower than -3 o C. Leaf area index changes between LAI min and LAI max (Table ) as a function of thermal-time DD (degree-days). The growth rate, g, is calculated as: 5

6 BEE 670 Spring 00 () g = The LAI is: DD DD DD 0.6 DD DD DD DD DD DD DD DD DD max 3 DD 0 DD DD (3) LAI LAI g LAI LAI min max Early growth Rapid growth min Full grown Senescence Dormant [-] This growth model can also be used for root growth between Z r-min and Z r-max, recognizing that some ecosystems will develop over a number of years to a maximum level and should probably not be returned to a minimum depth at the end of each season. Similarly, for very long simulations, the landscape may go through long-term ecological succession changes that need extra consideration. References: Beadle, C.L., Talbot, H. and Jarvis, P.G., 98. Canopy structure and leaf area index in a mature Scots pine forest. Forestry, 55: Dickinson, R. E., Henderson-Sellers, A., Rosenzweig, C., Sellers, P. J., 99: Epotranspiration models with canopy resistance for use in climate models: a review.forest Agric. Meteor.,5, Dingman, S.L., 00: Physical Hydrology, nd Ed.: Upper Saddle River, New Jersey. Prentice Hall. Easton, Z.M., P. Gérard-Marchant, M.T. Walter, A.M. Petrovic, T.S. Steenhuis Hydrologic assessment of an urban riable source watershed in the Northeast United States. Water Resources Research 3(3): Art. No. W033. Feddes, R.A. and P.E. Rijtema. 97. Water withdrawl by plant roots. Journal of Hydrology 7: Frankenberger, J.R., E.S. Brooks, M.T. Walter, M.F. Walter, T.S. Steenhuis A GIS-based riable source area model. Hydrological. Processes 3(6): Goudriaan, J. and H.H. n Laar. 99. Modelling potential crop growth processes. Kluwer Academic Publishers, Dordrecht, The Netherlands, 99. pp. 38. Jarvis, P.G The interpretation of the riations in leaf water potential and stomatal conductance found in canopies in the field. Phil. Trans. R. Soc. Lond., Ser. B 73: Monteith, J.L Eporation and environment. Symp. Soc. Exp. Biol. 9: 05-. Stewart, J.B Modeling surface conductance of pine fores. Agricultural and Forest Meteorology. 3(): Wigmosta, M., L. Vail, D. Lettenmair, 99. A distributed hydrology-vegetation model for complex terrain. Water Resources Research, vol. 30 no. 6, pp