A.G.C.A. Meesters

Analytical derivation of the vegetation optical depth from the microwave polarization difference index

A numerical solution for the canopy optical depth in an existing microwave-based land surface parameter retrieval model is presented. The optical depth is derived from the microwave polarization difference index and the dielectric constant of the soil. The original procedure used an approximation in the form of a logarithmic decay function to define this relationship and was derived through a series of lengthy polynomials. These polynomials had to be recalculated when the scattering albedo or antenna incidence angle changes. The new procedure is computationally more efficient and accurate.

Solving the production-diffusion equation for finite diffusion domains of various shapes Part I. Implications for low-temperature (U-Th)/He thermochronology

Abstract We propose an accurate, fast and easy-to-use method to derive numerical solutions for production–diffusion equations for finite diffusion domains of various shapes and arbitrary cooling histories. Previous studies provide solutions for spheres, infinite cylinders and infinite sheets. We extend this range and provide solutions for finite bodies, i.e. finite cylinders and rectangular blocks of any aspect ratio. This approach is important as recently, it has become clear that, for example, the physical grain is the diffusion domain for He diffusion in apatite and titanite [J. Geophys. Res. 105 (2000) 2903; Geochim. Cosmochim. Acta 63 (1999) 3845]. We discuss the use of the new approach for forward modelling (U–Th)/He production–diffusion in apatite. Taking results with finite cylinders as a good approximation for apatite crystals, it is found that approximating instead with spheres or infinite cylinders having the same radius yields differences in calculated ages that can easily be as large as 20–35%. The relative differences are most pronounced in thermal histories that spend significant time at or near the closure temperature. On the other hand, reasonable agreement is found with spheres having the same surface to volume ratio.

Solving the production -diffusion equation for finite diffusion domains of various shapes part 2, Application to cases with Alpha ejection and non-homogeneous distribution of the source

Abstract In this paper, numerical methods derived in Part I (Chem. Geol. (2002)) are expanded to accommodate the effects of α-emission and zonation of U and Th as relevant for (U–Th)/He thermochronology. Expressions for the required coefficients are derived for spheres, finite and infinite cylinders and rectangular blocks, for parent nuclide distributions, which are either uniform or have stepwise zoning. We show that the effects of α-emission and zonation on the He retention in a nonspherical crystal of modest aspect ratio can be approximated by a sphere of identical surface-to-volume ratio ( S / V ) if the zonation is transposed on to the sphere. The currently usual correction method is to perform first a diffusive calculation without considering α-emission and zonation and to multiply afterward with a correction factor that has been derived originally for nondiffusive calculations. Our results demonstrate that more accurate calculations yield different results and that the differences are often too large to be ignored in practice. Especially for thermal histories that include a protracted residence in the partial retention zone, the difference between the usual correction and our correction can be as high as ∼20% for homogeneous sources. For zoned crystals, the difference can be even larger.

Error Estimates for Near-Real-Time Satellite Soil Moisture as Derived From the Land Parameter Retrieval Model

A time-efficient solution to estimate the error of satellite surface soil moisture from the land parameter retrieval model is presented. The errors are estimated using an analytical solution for soil moisture retrievals from this radiative-transfer-based model that derives soil moisture from low-frequency passive microwave observations. The error estimate is based on a basic error propagation equation which uses the partial derivatives of the radiative transfer equation and estimated errors for each individual input parameter. Results similar to those of the Monte Carlo approach show that the developed time-efficient methodology could substitute computationally intensive methods. This procedure is therefore a welcome solution for near-real-time data assimilation studies where both the soil moisture product and error estimate are needed. The developed method is applied to the C-, X-, and Ku-bands of the Aqua/Advanced Microwave Scanning Radiometer for Earth Observing System sensor to study differences in errors between frequencies.

Automated separation of touching grains in digital images of thin sections

The determination of textural properties of granular material with image analysis is generally troubled by the fact that touching grain sections merge into single features. Without separation of these touching grain sections, the textural properties derived from the images contain substantial bias. Existing methods for separating touching grains, like erosion-dilation cycles or watershed segmentation, are time-consuming and/or alter the textural properties of the grain sections analyzed. An alternative computer algorithm is presented to separate touching grain sections in binary images of granular material. The algorithm detects characteristic sharp contact wedges in the outline of touching grain sections and creates an intersection after checking if the angle of the contact wedge is smaller than a user-defined threshold value. The performance of the new algorithm is compared to that of the watershed segmentation method. The resulting grain-size distributions after applying automated separation techniques, were verified with the size distribution obtained with a laboratory laser particle sizer. The algorithm shows improved preservation of size and shape characteristics of the granular material over the watershed segmentation method.

Inverse carbon dioxide flux estimates for the Netherlands

CO2 fluxes for the Netherlands and surroundings are estimated for the year 2008, from concentration measurements at four towers, using an inverse model. The results are compared to direct CO2 flux measurements by aircraft, for 6 flight tracks over the Netherlands, flown multiple times in each season. We applied the Regional Atmospheric Mesoscale Modeling system (RAMS) coupled to a simple carbon flux scheme (including fossil fuel), which was run at 10 km resolution, and inverted with an Ensemble Kalman Filter. The domain had 6 eco-regions, and inversions were performed for the four seasons separately. Inversion methods with pixel-dependent and -independent parameters for each eco-region were compared. The two inversion methods, in general, yield comparable flux averages for each eco-region and season, whereas the difference from the prior flux may be large. Posterior fluxes co-sampled along the aircraft flight tracks are usually much closer to the observations than the priors, with a comparable performance for both inversion methods, and with best performance for summer and autumn. The inversions showed more negative CO2 fluxes than the priors, though the latter are obtained from a biosphere model optimized using the Fluxnet database, containing observations from more than 200 locations worldwide. The two different crop ecotypes showed very different CO2 uptakes, which was unknown from the priors. The annual-average uptake is practically zero for the grassland class and for one of the cropland classes, whereas the other cropland class had a large net uptake, possibly because of the abundance of maize there.

Calculation of heat storage in stems

A method for calculating heat storage in tree stems from measured ambient air temperatures is described. The method is easy to use also for sites where the variation in the stem radii is large. The results are exact provided the thermal properties of the stems are constant, the temperature field within the stems has radial symmetry, and the stems are in radiative equilibrium with their surroundings. Either the stem surface temperature or the temperature of the surrounding air can be used as input. For the latter case, an exact solution involving a surface resistance is derived. The method has been applied to a pine plantation in Fiji, where the calculated heat storage was compared to the storage inferred from the measured stem temperatures. Despite non-ideal conditions, the overall correspondence is good.

Turbulence observations above a smooth melting surface on the Greenland ice sheet

Measurements of profiles and turbulent fluxes havebeen made over a smooth, melting surface on thesouthwestern part of the Greenland ice sheet in July1991. For a reference height of 0.8 m, and fluxmeasurements at 4 m and 13 m, the best values for theroughness lengths are 3 × 10-4 m for wind speed,2 × 10-6 m for temperature, and 5 × 10-4 mfor moisture. The uncertainty in the correspondingexchange coefficients is about 10%. The roughnesslength for temperature (zT) is much smaller than expectedfrom theory, as was also found in a number of earlierinvestigations. The possibility is considered thatabsorption of shortwave radiation by aerosol particlesaccumulating near the surface lowers thezT values. Consequently, zT using lower measurementheights should probably be close to z0.However, evidence for this remains rather indirect.Further, it is shown that reliable results for thesensible heat flux can be obtained using the productof the observed standard deviation for temperature fluctuationsand wind speed.

Optimum vegetation characteristics, assimilation, and transpiration during a dry season: 2. Model evaluation

Received 8 June 2007; revised 3 December 2007; accepted 12 December 2007; published 21 March 2008. [1] In a companion paper, a conceptual model was presented to predict two important vegetation parameters from climatic constraints in water limited conditions, notably photosynthetic capacity and internal carbon dioxide concentration. In this study, the model is evaluated using data of four experimental forest plots in sub-Mediterranean Slovenia which were selected for their topography induced differences in climate and contrasting vegetation characteristics. Data were collected during a regular (2004) and an exceptionally dry year (2003). Measurements showed that photosynthetic capacity decreases with vapor pressure deficit, and internal carbon dioxide concentration correlates positively with available water. Variations in soil water storage at the start of the dry season and vapor pressure deficit during the dry season are responsible for a large part of these differences. Winter precipitation has a large effect on the shape of the seasonal course of transpiration during the following season. The model explained observed differences among sites and years in photosynthetic capacity and the seasonal cycle of transpiration. Although the magnitude of calculated optimum internal carbon dioxide concentrations agreed with observations, the model could not explain observed differences in internal carbon dioxide concentration or the correlation between internal carbon dioxide concentration and water availability. The optimality hypothesis, despite its limitations, can be used to predict the seasonal cycle of transpiration.

A case study of the daily energy balance near the equilibrium line on the Greenland ice sheet

Abstract This paper presents the energy balance for two specific days during the summer of 1991 at the camp of the Vrije Universiteit Amsterdam (VU-Camp) on the Greenland ice sheet. On the basis of this energy balance the amount of melt for both days is estimated. This amount is compared with the melt as measured at the position of two snow stakes. Although numerous difficulties are associated with the interpretation of stake measurements, both methods are seen to agree within experimental error.