Dual-source Model Research Articles

Dual versus single source models for estimating surface temperature of African savannah

Abstract. Predictions of average surface temperature of a sparsely vegetated West-African savannah by both single and dual source models of surface energy partitioning are compared. Within the single source model, the ``excess resistance" to heat transfer away from the canopy (compared to momentum absorption) is characterised by parameter kB-1, where k is the von Kármán constant and B is the Stanton number. Two values of this parameter are used; first kB-1 = 2 (a value often used within surface energy balance models but primarily applicable to permeable vegetation types) and then 12.4 (a value applicable to the savannah in question, which consists more of bluff roughness elements). As expected, the latter parameterisation generates better predictions of surface temperature. To make accurate predictions of surface temperature using a dual source model, then that model’s in-canopy aerodynamic resistance must be increased. Information on this increase is found through direct model intercomparison with the single source model parameterised with kB-1 = 12.4. Keywords: Penman-Monteith equation; Surface temperature; Canopy resistance; Savannah; Dual-Source model

A model study of kBH−1 for vegetated surfaces using ‘localized near-field’ Lagrangian theory

Models of energy and mass exchange between vegetation canopies and the atmosphere usually include some formulation of the bulk boundary layer resistance ( R b or the related parameter kB −1) to describe the effects of molecular diffusion occurring near the leaf and soil surfaces. Present formulations of kB −1 are either empirical expressions or are physically based models derived from a K-theory approach. However, K-theory does not describe the observed counter gradient flow within canopies and the empirical expressions usually lump both canopy and soil effects into a single surface resistance (single source approach). For areas of partial canopy cover, single source formulations have been difficult to formulate with any certainty and often do not agree with observations. This study uses ‘localized near-field’ (LNF) Lagrangian theory to develop a model of kB −1 (for heat transfer) for the vegetation component of a dual source model and for the combined effects of canopy and soil in a single source approach. The present model also uses a physically based, one-dimensional, analytical model to describe the influence of canopy structure and density upon the within-canopy far field diffusivity and Lagrangian time scale which are central to the LNF Lagrangian theory. The canopy turbulence model is designed for arbitrary foliage structure and density and kB −1 is defined in terms of heat and momentum fluxes rather than the more conventional logarithm of the ratio of the momentum and thermal roughness lengths. The resulting kB −1 model is used for sensitivity studies of kB −1 for canopies only (i.e. no soil contribution) and for the coupled canopy–soil system (i.e. a single source model). Results indicate that foliage density (Drag Area Index or Leaf Area Index), wind speed, leaf size, possible sheltering effects, and, to a lesser extent, the vertical foliage distribution and the vertical variation of the temperature difference between the foliage and the near-leaf air space can influence kB −1. For the single source model the soil boundary layer resistance was found to be significant for areas of partial canopy cover. In spite of the relative complexity of the full LNF model of kB −1, a simple expression that varies smoothly between bare soil and full canopy cover is developed that captures much of the modeled and observed variation in kB −1 for the single source approach.

Combining Optical and Microwave Remote Sensing for Mapping Energy Fluxes in a Semiarid Watershed

A dual-source model treating the energy balance of the soil/substrate and vegetation that was developed to use radiometric surface temperature observations is revised to use remotely sensed near-surface moisture from a passive microwave sensor for estimating the soil surface energy balance. With remotely sensed images of near-surface soil moisture, land cover classification, and leaf area index, the model is applied over a semiarid area in the Walnut Gulch Watershed in southern Arizona. The spatial and temporal variation of the Bowen ratio (i.e., the ratio of the turbulent fluxes, sensible, and latent heat) “maps” generated by the model were similar to the changes in near-surface moisture fields caused by recent precipitation events in the study area. The estimated fluxes at the time of the microwave observations (i.e., “instantaneous” estimates) and those simulated over the daytime period are compared with the ground observations within the watershed. Differences between predicted and observed “instantaneous” fluxes were usually comparable to the measurement uncertainties, namely, 5% for net radiation and 20–30% for soil, sensible and latent heat fluxes, except when there was large temporal and spatial variations in solar radiation across the study area. However, by running the model over the daytime period, this variability in solar radiation proved to have a minor effect on computed daytime totals. In fact, differences with observed heat fluxes were significantly less (i.e., around 15%) than when comparing “instantaneous” values. Model predictions of the total soil heat flux over the daytime period were generally higher than measured. An empirical model was developed to reduce this bias, but it is not known how generally applicable it will be. Model sensitivity to typical uncertainties in remotely sensed leaf area index (LAI) and near-surface (0–5 cm) water content, W, was quantified. The variation in flux predictions caused by errors in prescribing leaf area index and W was less than 30%. More tests with this model over different landscapes are necessary to evaluate its potential for predicting regional fluxes. In particular, microwave and radiometric surface temperature observations are needed under drought conditions for evaluating if the model formulation of vegetation transpiration can properly adjust to this extreme and very important environmental condition.Published by Elsevier Science Inc., 1998

Calculating dose and output factors for wedged photon radiotherapy fields using a convolution/superposition method.

We have developed a convolution/superposition method to calculate dose distributions in photon treatment fields with beam modifiers such as physical wedges. The dose component due to wedge generated radiation was accounted for by using an extended phantom model, which integrated a wedge, an air gap, and a patient phantom as the calculation phantom. The inhomogeneities in the extended phantom and the effect of beam hardening by the wedge were both corrected for in the convolution dose calculation. The calculated dose was verified by Monte Carlo simulation of the same extended phantom. A new dual photon source model was also used in the convolution method to account for both primary photons from the target and extra-focal photons from the primary collimator and flattening filter. Thus, realistic photon energy fluence distributions in the extended phantom were used for the dose calculation. The calculated dose distributions and the wedge factors agreed with the measured data within 2% for a variety of treatment fields including asymmetric fields. Our results showed that the wedge-generated radiation could contribute a significant fraction of the total dose in patients. This dose component depends on a specific field configuration, thus wedge factor changes with photon energy, wedge angle, field size, depth, and patient phantom SSD. The variation of the wedge factor can be predicted accurately by our convolution approach with the extended phantom model, which allows for more accurate dose or monitor unit computation for photon fields with beam modifiers.

An intercomparison study on models of sensible heat flux over partial canopy surfaces with remotely sensed surface temperature

Using remotely sensed surface temperature to estimate the sensible heat flux over partial canopy covered surfaces, one faces the problem of how the bare soil and plant foliage temperatures contributing to the radiometric surface temperature are related to the turbulent transport of sensible heat across the surface-atmosphere interface. To solve this problem, several sensible heat models, using radiometric surface temperature, have appeared in the literature. In this study, using the observational data from three interdisciplinary field experiments [the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE), Monsoon '90 and Washita '92, the performance of four models using average values of their parameters in predicting land surface sensible heat flux was evaluated. By analyzing the sensitivity of the models to common parameters and input variables, reasons for differences in the performances of the models and the potential to improve the agreement with observations have been ascertained. From the comparisons of modeled versus measured sensible heat flux for the different surfaces, the dual-source model in Norman et al. (1995) had the best agreement with its mean absolute percent difference (MAPD) values being similar to the observational accuracy (i.e., ∼ 20%). From the sensitivity analysis the model appears to have the greatest potential for operational applications since it requires relatively few parameters and is not very sensitive to the uncertainty in most of the model parameters. The single-source models in Kustas et al. (1989) and Troufleau et al. (1996) require accurate estimates of the surface roughness z 0m and empirical relationships to account for differences between aerodynamic and radiometric temperature. Therefore, it may be difficult to improve their performance without some independent means of estimating the empirical coefficients and a reliable method for determining z 0m. Estimates from the dual-source model in Lhomme et al. (1994) tend to produce the largest scatter with the observations. This may be related to the fact that the model is more sensitive to variations in most of the parameters common in dual-source models. In addition, its response to high surface-air temperature differences in the sensitivity analysis differs from all other models. Therefore, it may be more difficult to obtain reliable estimates from this model on an operational basis.

Single- and Dual-Source Modeling of Surface Energy Fluxes with Radiometric Surface Temperature

Abstract Single- and dual-source models of the surface energy transfer across the soil-vegetation-atmosphere interface were used in conjunction with remotely sensed surface temperature for computing the surface energy balance over heterogeneous surfaces. Both models are relatively simple so that only a few parameters are specified, making them potentially useful for computing surface fluxes with operational satellite observations. The models were tested with datasets collected from a semiarid rangeland environment with canopy cover generally less than 50% and a subhumid tallgrass prairie environment having canopy cover typically greater than 50%. For the semiarid site, differences between the single-source and dual-source model estimates of the sensible heat flux (H) and the observations averaged about 25%. For the tallgrass prairie, the disagreement between observations and single-source model estimates of H was significantly larger, averaging nearly 55%. The average difference between observations and t...

Bidding for Contests

The procurement of product development and production services brings special strategic considerations to the buyer-seller relationship in industrial and institutional markets. Multiple sourcing, in particular dual sourcing, is a likely way of dealing with the increased risks faced by buyers. However, there is lack of dual sourcing models that analyze the selection and control process in an integrated fashion. This omission had led to apparently contradictory findings in agency and auction theory. The paper models the strategic issues for a cost containment contest between two suppliers. The suppliers are drawn from several vendors who participate in a bidding competition. The supplier with the lower final cost in the contest wins a larger share of the pooled profit fee. Propositions are derived for the optimal cost-plus contest, and comparisons are made with the common incentive contract for the integrated selection and control model. The larger the winner's share, the greater the effort. The buyer can make a credible commitment to the optimal winner's share. As the winner's share rises, however, the bid prices increase due to increased contract risk. This incentive-risk tradeoff determines (a) the optimal winner's share that minimizes expected procurement price, (b) the corresponding profit fee bid by suppliers, (c) the ensuing cost control effort, and (d) the final price for the procurement. Comparisons with the common incentive contract tell us when the cost-plus contest induces more effort, and when bidding for a contest results in a lower final procurement price.

The Roughness Length for Heat of Sparse Vegetation

Abstract A dual-source model that solves the energy balance over vegetation and soil separately can be inverted to obtain the roughness length for heat z0h of a single-source model. Model parameters for the dual-source model were taken from previous analysis of data from a sparse canopy in semiarid terrain. In these circumstances, the value of z0h, is shown to be dependent on the humidity deficit, the available energy, the vegetation fraction, and the surface resistance of the soil and the vegetation.