1. Abstract Estimating thermal diffusivity from imagery 1 Contact information Angular variations in emmissivity A ground-based, multi-spectral imaging system (thermal infrared, visible, near-infrared) enables quantification of natural processes within the critical zone at high spatial (0.1 to10 cm) and temporal (> 1Hz) resolution. Thermal imaging takes advantage of the tight coupling between the water and energy budgets using heat as a tracer of hydrological processes. We are developing analytical techniques to transform apparent radiant temperatures measured at oblique angles into absolute kinetic temperatures to enable estimation of thermal properties of water, sediment, and biological mixtures using the spatial and temporal variations in surface temperature. The key transformations involve removing the strong variations in apparent temperature due to angular variations in material emissivity, estimating emissivity of different materials in the image and minimizing effects of thermal noise from background radiators. Classification of visible and near-infrared images constrains transformations and interpretations of the thermal images by allowing identification of materials that may have different radiant properties (emissivity/reflectivity) and identifying background radiators that add noise to the thermal images. We performed experiments in the laboratory using water and sediments (mud/sand/gravel) to quantify decreases in emissivity and apparent temperatures in thermal imagery due to oblique viewing angles. An algorithm was developed to create an emissivity map at the pixel scale so apparent temperatures in images can be transformed into kinetic temperatures (Figure 1). The thermal diffusivities of point bar sediments along a coastal plain river were estimated by fitting an analytical solution of the 1-D, transient heat- conduction equation to time series of surface temperatures in three regions of interest from a sequence of thermal images collected on 15-minute intervals over 24 hours. Remotely determined diffusivities were validated using estimates obtained by analyzing time series from two subsurface thermistor arrays (8 sensors from 3 cm to 35 cm depths). Application in biogeochemistry Estimating thermal diffusivity from imagery 2 Transforming Ground-Based Oblique Thermal Images to Enable Quantitative Analysis of Coupled Heat and Fluid Flow in the Critical Zone Thomas E. McKenna, Delaware Geological Survey, University of Delaware Timothy E. Sliwinski * and Jack A. Puleo, Center for Applied Coastal Research, University of Delaware *currently at Bechtel Power Corporation, Frederick, MD H41D-1067 Center for Applied Coastal Research Tom McKenna Delaware Geological Survey, University of Delaware Newark, Delaware 19716 302-831-8257 ; mckennat@udel.edu Tim Sliwinski: tsliwins@bechtel.com Jack Puleo: j puleo@udel.edu ROI thermal effusivity W s 1/2 m -2 K -1 thermal diffusivity m 2 /s North12891.35e-6 South12181.52e-6 Sand12081.54e-6 During darkness, imaged sands cool faster than imaged mud draped over sand. After sunrise, the opposite occurs. Temperature trend of in situ sensors at 3-cm depth are warmer than imaged surface at night and cooler than imaged surface in daytime. compact sand (in situ) darkness visual image taken the following day at low tide 11:34 pm 11:10 pm 10:45 pm Thermal images of ebbing tide showing warm (red) tidal water flowing out of a colder (blue) salt marsh on a summer evening (June 2009) in Delaware, USA. 30 m 20 22 °C°C 1218 °C°C 6:34 DST 60 7:34 DST 120 5:49 DST 15 6:04 DST 30 6:19 DST 45 8:04 DST 150 8:19 DST 165 min135 7:49 DST 90 7:04 DST 105 7:19 DST sunrise 5:34 DST 0 min flood tide 75 6:49 DST high tide ebb tide Cooler water from the Delaware Bay flows into a tidal channel during flood tide and back out during ebb tide (May 2008) visual Estimates of marsh inundation are being used to estimate fluxes of nutrients and dissolved oxygen to and from salt marshes. visualthermal (raw) thermal (corrected) Lab experiment with thermal imager (7.5- 13 μm) viewing water at multiple angles Above: Measurements are in good agreement with predictions using Fresnel relationship for angles less than ~75 degrees from nadir. Below: Thermal image (nominal angle = 65 o ) corrected for angular emissivity variation determined above. Correcting field imagery taken at oblique angles quartz sand Visual image showing the field of view (FOV) of the thermal imager. The cooling of the earth’s surface on a clear, windless night (like at the field site) can be approximated by the removal of heat at a constant heat flow density. The solution for transient heat conduction in a semi-infinite solid with a constant surface heat flow density is (Carslaw and Jaeger, 1959): The transient surface temperature is T (z, t) = temperature at depth z and time t F 0 = constant heat flow density at the sediment surface (z=0) α′ = thermal diffusivity k = thermal conductivity e = thermal effusivity = sqrt (k 2 /α′) F 0 is estimated from the net radiometer data. Assuming that the heat flow density is similar for the three ROIs during the nighttime cooling, the slopes of straight line fits on a plot of surface temperature versus the sqrt (time) give robust estimates of the thermal effusivity. If we also assume a similar thermal conductivity for the three ROIs, thermal diffusivity can be estimated. Thermal diffusivity values calculated using this method with the imagery have the same order of magnitude as those determined by inverting numerical and analytical models using time series from the in-situ temperature profilers, suggesting that this method shows promise for remote determination of sediment thermal properties. Presented at the 2011 Annual Meeting of the American Geophysical Union (Session H41D: Geophysics for the Critical Zone) 1/2 Remote sensing data: images of point bar sediment every 15 minutes for ~2 days using visual and thermal infrared imagers mounted on a radio tower installed on the river bank (orange rectangle is the field of view) imagers water visualthermal (raw) thermal (corrected) visualthermal (raw) thermal (corrected) Measurements and predictions in good agreement for water and sand at angles < ~80 degrees from nadir. water increasing angle and distance quartz sand increasing angle and distance Three regions of interest (ROI) were defined within the FOV based on lithology. The mean temperature (spatial) was calculated for each region of interest (ROI) at each15-minute interval and compared to in-situ temperatures (below. mud drape over sand compacted silty sand unconsolidated sand North temp. profiler South temp. profiler 3 m In situ data: time series at 5-minute intervals of subsurface temperature (including two profiles of 8 sensors at 3 to 30 cm depths), soil moisture, net solar radiation, air temperature, wind speed and direction, and humidity Conclusion