Wang, J., T.W. Sammis, and V. P. Gutshcick, Inferring complex patterns of surface flux and atmospheric circulation via remote sensing. Flux Measurements in Difficult Conditions, a Specialist Workshop. Boulder, Colorado, USA, January 2006.

Inferring complex patterns of surface flux and atmospheric circulation via remote sensing Introduction Lack of energy closure in eddy covariance measurements casts doubt upon our understanding of both atmospheric and biophysical control of surface fluxes. Poor closure may arise from limitations in instrumental responses, as well as from advection and other complex air circulations in inhomogeneous terrain. Inhomogeneity increases with spatial extent sampled by towers, and thus it increases under the troublesome stable conditions. Improved understanding of atmospheric circulations will be aided if we can quantify the spatial pattern of surface scalar fluxes of sensible and latent heat. However, the spatial pattern of fluxes is poorly inferred from tower flux measurements, which comprise a convolution over the pattern (as well as having the compromised accuracy that is the subject of the inquiry). Inversion of the flux to spatial pattern is an ill-conditioned problem that defies useful solution. More direct estimates of spatial patterns in fluxes may be obtained using remote sensing. One remote sensing method of sufficiently high spatial resolution for LE (ET) is a version of the surface energy balance method (modified from [Bastiaanssen et al., 1998]). Spatial patterning of ET is evident at 90-m resolution (see “Results”). We also offer an extension to CO 2 flux estimation, using ET to infer stomatal conductance that may be used to correct radiation-use efficiencies. With satellite data, the energy-balance methods are limited to daytime conditions, but the method could be used with finer spatial and temporal sampling by deploying inexpensive infrared thermocouples. Junming Wang, Vincent P. Gutschick, Theodore W. Sammis New Mexico State University, Department of Agronomy and Horticulture References Bastiaanssen, W. G. M., M. Menenti, R. A. Feddes, and A. A. M. Holtslag, 1998: A remote sensing surface energy balance algorithm for land (SEBAL). 1. Formulation. J. Hydrol., 212/213, Kustas, W. P., & Norman, J. M. (2000). A two-source energy balance approach using directional radiometric temperature observations for sparse canopy covered surfaces. Agronomy Journal, 92(5), 847–854. Wang, J., T.W. Sammis, C.A. Meier, L.J. Simmons, D.R. Miller, and Z. Samani A modified SEBAL model for spatially estimating pecan consumptive water use for las cruces, new mexico. 15th Conference on Applied Climatology. Hilton Savannah DeSoto, Savannah, Georgia June, Acknowledgments: Research partially funded by New Mexico Agricultural Experiment Station, Rio Grande Initiative and USDA Forest Service. Objective: 1)Develop a remote sensing model to estimate spatial ET distribution and give guidelines to set up flux towers or test if a ET measurement at a location can represent the values at that area, 2)Use spatial ET data to infer CO 2 flux, 3) Sense high spatial and temporal variation in ET and CO 2 Fluxes. Conclusions The RET model is capable to map spatial ET with a resolution 90 m by 90 m. The RET model is capable to give guidelines to set up ET measurement towers and check that if a ET measurement at a location represents the values at that area. Spatial ET can be used to infer the spatial CO 2 fluxes. Sensing high spatial and temporal ET is possible using satellite data and high spatial and temporal-density infrared data. Method: Remote sensing model A Remote Sensing ET model (RET) written in c++ program language was developed. The model can estimate ET in 90 m  90 m resolution using ASTER satellite and local weather data. ASTER data was obtained from NASA Earth Observing System Data Gateway ( welcome/). The model general flowchart is shown in Figure 2. Inputs The inputs include wind speed, humidity, and solar radiation data at the local weather station and satellite data products from ASTER, including ground surface reflectance and temperature. The reflectance has a resolution of 15 m  15 m for the bands 1 to 3 (Visible and Near-infrared bands) and 30 m  30 m for the bands 4 to 9 (Shortwave Infrared bands). The temperature data has a resolution 90 m  90 m. Each satellite scene covers an area of 60 km by 60 km. The reflectance data were averaged over 90 m  90 m to match the temperature data resolution. Outputs The spatial ET (mm d -1 or mm h -1 ) is the output from the model. The resolution is 90 m  90 m. Model theory Rn is net radiation (W m -2 ), Rns is net short-wave radiation (W m -2 ), Rnl is net long-wave radiation (W m -2 ). where:  is surface albedo (calculated from reflectance), Rs is incoming solar radiation measured at the local weather station (W m-2). C is a function of NDVI (normalized difference vegetation index) (Figure 3, Bastiaanssen et al., 1998 ) NDVI is calculated as follows: where α 3 and α 2 are the reflectance data of bands 3 and 2 respectively. Where  is the air density (mol m -3 ), cp is the specific heat of air (29.3 J mol -1 ºC -1 ), dT is the near surface temperature difference (K), r ah is the aerodynamic resistance to heat transport (s m -1 ), where dT is calculated according to dT values at a hot and a cold spot (Wang et al., 2005). H calculations need atmospheric correction (Figure 4). Figure 6. The flux tower site at Blodgett Forest, CA. Latitude: 38° 53' 42.9" N Longitude: 120° 37' 57.9" W Figure 1. Flux measurement towers. Picture from Figure 5. Jornada Experimental Range landscape. ARS pilot Michael René Davis flies the Cessna over the Jornada Range. Photo by Scott Bauer. Latitude: N. Longitude: W. aug01/k htm Figure 2. The RET model flow chart. Figure 3. Relationship of C = soil heat flux/net radiation, with NDVI. Data are from Clothier et al. (1986), Choudhury (1989), Kustas and Daughtry (1990), Van Oevelen (1993) and Bastiaanssen et al. (1998). Figure 4. Atmospheric correction for H. At the Blodgett tower, the ET from RET calculation is 0.40 mm h -1 vs mm h -1 with the tower measurement at 11:30am local time (Central America time zone, GMT time 19:30pm) on August 13, 2001 (Figure 8). The tower measurement represents the fluxes along the 270 m distance in the southwest direction of the tower. The wind direction in daytime is from southwest to northeast. The average flux of the pixels at this distance was 0.36 mm h -1 and standard deviation was 0.03 mm h -1. However, the tower measurement does not represent other sides’ ET flux. The surrounding pixels in other sides (total 5) had average daytime ET of 0.57 mm h -1 and standard deviation was 0.04 mm h -1. N Results Remote sensing model The ET map shows the Jornada rain track (Figure 7). ET distribution was quite different among the pixels from differences in land cover. Study sites: Two sites are chosen to be studied. One is the Jornada Experimental Range in New Mexico (Figure 5). The site has mesquite and other shrubs. ASTER satellite data was obtained for September 17 th Two days before this scene it rained. This data set is processed here to determine the ET distribution after rain. The other site is an Ameriflux site, the flux tower site at Blodgett Forest, CA. The site is situated in a ponderosa pine plantation within a mixed-evergreen coniferous forest, located adjacent to Blodgett Forest Research Station. The plantation is relatively flat, and contains a homogenous mixture of 5 to 7 year old (in 1997) ponderosa pine with other trees and shrubs ( ASTER satellite data on August 13, 2001 was obtained and is processed to test if the tower ET measurement represents the values at its area. Figure 7. Evapotranspiration (ET) estimated from remote sensed hourly ET for Jornada (desert area), Las Cruces, New Mexico on a summer day of The ET map shows ET spatial variability in the absence of terrain variability. The resolution is 90 m by 90 m and the scale is 50 km by 35 km (Height by width). The tower location. Using ET to infer CO 2 flux Premises: 1) Both A (CO 2 assimilation) and E (or ET) arise from the combination of physiological and meteorological control. At a given meteorological condition (solar flux density; air temperature, humidity, and pressure; windspeed; downwelling TIR flux density or effective sky temperature), physiological control sets stomatal conductance g s, leaf temperature T L, A, and E. The relationships are set by three process equations: A) leaf energy balance, in which g s, along with meteorological variables, sets T L ; B) stomatal control program, taken as well represented by the Ball-Berry equation (Ball et al., 1987; see Gutschick and Simonneau, 2002): g s = m A h s / C s + b; m, b = robust empirical constants (m very near 10 for all unstressed leaves of plants with dominant C3 pathway of photosynthesis), h s and C s = relative humidity and CO 2 mixing ratio at surface of leaf, under the leaf boundary layer; C) enzyme-kinetic equation for A, well represented by the model of Farquhar et al. (1980 ff.) - at light-saturation (ca % of all assimilation), A = V c,max (C i -Γ)/(C i +K CO ), where V c,max = photosynthetic capacity (A at light- and CO 2 -saturation; set by enzyme investment that acclimates to environment under genetic constraints; predictable for vegetation types), Γ=compensation partial pressure of CO 2, a function only of temperature and O 2 partial pressure, as also is K CO, an effective Michaelis constant. These three transcendental equations can be solved simultaneously by numerical methods (Gutschick, unpubl.) 2) Water stress has its dominant effect on the stomatal control parameter, m, in the short term (days); for long stress, the effect extends to photosynthetic capacity, V c,max. Both of these types of physiological changes alter both A and E. Effectively, water stress reduces g s, consequently reducing leaf-internal CO 2 partial pressure and the radiation-use efficiency of leaves; A decreases at constant photon flux density. 3) We can predict spatial and temporal variations in A from observable spatial and temporal variations in E, if the relationship of A to E is sufficiently strong and also robust. By “robust”, we mean that it has only moderate dependence upon initial physiological variations (some plants have m moderately above or below 10 when unstressed, while their value of intercept b differs in the opposite direction: high m, low b). We simulated g s, T L, A, and E under the same meteorological conditions, representative of Eastern deciduous forests1, while varying 1) m, with b constant - representing moderate-term water stress of increasing degree; 2) V c,max, with m and b at original values - representing different species of different intrinsic growth rate, OR variations in nitrogen stress; 3) V c,max with low m = 5 - representing the same species under water stress; 4) initial m (from 12 to 8), with b countervarying from 0.02 to representing species differing in stomatal control. Sensing high temporal and spatial ET flux Supplementing satellite imagery with local sensing of surface temperatures: The temporal and spatial resolution of satellite imagery (in the critical thermal infrared) is necessarily modest, at 1 km x 1 day (MODIS) or 120m x 16 days (ASTER). Even daily resolution requires modelling of the diurnal time course of ET to estimate daily total ET. The 16-day resolution of ASTER misses short-term events that dominate in drier environments. The most challenging data to fill in temporally and spatially is the thermal infrared data. In contrast, downwelling shortwave and longwave radiation varies little spatially in the absence of clouds and both can be extrapolated from sparse station measurements. Similar considerations hold for the other principal meteorological drivers, air temperature and humidity and windspeed. Vegetation interception of radiation and also momentum transfer depend upon plant structure, which changes slowly in almost every landscape. Infrared thermcouples such as marketed by Apogee Instruments® can sense surface radiative temperature very accurately and minimal drift, while being relatively inexpensive and readily logged. The useful models have separate voltage outputs for target and body temperatures, allowing for correction of the apparent target temperature. While it is not practical to cover a large landscape with such sensors, a single sensor at a key site will allow accurate estimation of the diurnal course of ET. Sensors at key locations on a large transect will enable the testing of models of the spatial distribution of vegetation distribution and ET- altering water stress. ET to infer CO 2 flux 1) The curve of A (CO 2 assimilation) vs. E (ET) is smooth and relatively flat (Figure 9). The low slope is expected, in that reduction of g s affects E much more than it affects A; g s is almost all of the resistance for water vapor transport while it is a minor part of the resistance for CO 2 transport. 2) Consequently, A variations are predictable from variations in E. The effect of errors in estimating E upon errors in estimating A are modest. At moderately high stress (m reduced to 5), a 10% relative error in E (which is now at 60% of its original value) generates a 6% error in estimated A (which is at 79% of its original value). 3) Variations in V c,max exert stronger control over both A and E, and the A-E relation is steeper. The same curve does NOT apply as for water stress. One must use a different curve to predict A from E, so that one must know the different species (readily done, with field work) or that the variations within one species correspond to variations in nutrient stress (stress is relatively unlikely in natural conditions, though likely in agricultural conditions; in natural conditions, high N stress leads to replacement by other species competitively). 4) Variations among species in initial m values (optimistic vs. pessimistic stomata, we may say) do not alter the A-E curve at all. In the Figure 9, the curve of linked m-b variations is visually indistinguishable from simple variations in m alone. Consequently, there is promise in using remotely-sensed ET to estimate spatial and temporal variations in landscape CO 2 fluxes. Figure 9. CO 2 assimilation, A, and ET (E in the graph) relations under varying physiological stress. Sensing high spatial and temporal ET This work is being developed. mm d -1 mm h -1 Figure 8. Blodgett area ET map processed by RET model for August 13, The resolution is 90 m by 90 m.