Source Area Model Research Articles

Comparing Aircraft-Based Remotely Sensed Energy Balance Fluxes with Eddy Covariance Tower Data Using Heat Flux Source Area Functions

Abstract In an effort to better evaluate distributed airborne remotely sensed sensible and latent heat flux estimates, two heat flux source area (footprint) models were applied to the imagery, and their pixel weighting/integrating functionality was investigated through statistical analysis. Soil heat flux and sensible heat flux models were calibrated. The latent heat flux was determined as a residual from the energy balance equation. The resulting raster images were integrated using the 2D footprints and were compared to eddy covariance energy balance flux measurements. The results show latent heat flux estimates (adjusted for closure) with errors of (mean ± std dev) −9.2 ± 39.4 W m−2, sensible heat flux estimate errors of 9.4 ± 28.3 W m−2, net radiation error of −4.8 ± 20.7 W m−2, and soil heat flux error of −0.5 ± 24.5 W m−2. This good agreement with measured values indicates that the adopted methodology for estimating the energy balance components, using high-resolution airborne multispectral imagery, is appropriate for modeling latent heat fluxes. The method worked well for the unstable atmospheric conditions of the study. The footprint weighting/integration models tested indicate that they perform better than simple pixel averages upwind from the flux stations. In particular the flux source area model (footprint) seemed to better integrate the resulting heat flux image pixels. It is suggested that future studies test the methodology for heterogeneous surfaces under stable atmospheric conditions.

Validation of footprint models using natural tracer measurements from a field experiment

Although footprint modelling has become an important and widely used tool in micrometeorology, the validation of existing models remains an outstanding problem. This study presents experimental approaches using natural tracer measurements to evaluate the performance of footprint models, which are intended to provide an inexpensive and practical alternative to footprint evaluation experiments releasing artificial trace gases. The approaches tested and discussed here are based on either eddy-covariance measurement complexes or small aperture scintillometers operated during field scale experiments in an area of well-defined heterogeneity. We tested two different footprint validation approaches based on natural tracer measurements: firstly, a comparison of measured flux differences and modelled land use differences for pairs of measurement positions and secondly, a correlation analysis between measured and modelled quantities using reference measurements. We tested these footprint validation approaches on two different footprint models, an analytical flux source area model and a forward Lagrangian stochastic trajectory model. For the test we utilised measurements from an intensive field scale measurement campaign from summer 2002 instead of performing a new experiment to derive the required data set. The results of this study clearly demonstrate that the two approaches tested here based on natural tracers provide a valuable tool for footprint validation purposes. The first approach highlighted qualitatively the agreement between flux differences and differences in the land use of the surrounding terrain determined by footprint calculations, while the second approach, the correlation analysis between measured and modelled quantities, also allowed the comparison of the two footprint models on a quantitative basis. However, due to experimental shortcomings of the employed data set, additional scatter compromised the accuracy of the results; therefore, no significant differences between both footprint models could be found in this study.

Variation Of Urban Momentum Roughness Length With Land Use In The Upwind Source Area, As Observed in Two U.K. Cities

The possibility of obtaining urban roughness length from satellite-derived maps of land cover is explored, using turbulence measurements taken above the urban canopy. The upwind land cover is identified using a source-area model. Firstly, from four sets of measurements taken in Birmingham (U.K.), it is shown that in an area mainly split between the land-cover types ‘urban’ and ‘suburban’, suburban cover in the upwind source area is the more important contributor to increasing measured roughness length. A smaller dataset obtained in a second U.K. city (Salford, Greater Manchester) shows a similar result. A roughness-length aggregation model is also applied to the data from both sites. This assigns values of roughness length to each of the land-cover classifications and uses the source-area model to predict the resultant roughness length based on the wind properties. The results from this are shown to agree with the earlier findings.

Modelling and managing critical source areas of diffuse pollution from agricultural land using flow connectivity simulation

A combined critical source area and flow accumulation model is described that predicts the spatial distribution in the risk of diffuse nutrient losses from agricultural fields reaching surface waters. The model is applied to a number of agricultural fields under a range of different land management scenarios. The model output highlights the importance of land management features such as tramlines, tracks and field drains in concentrating flow towards receiving waters and in increasing the risk of the delivery of pollutants derived from diffuse agricultural sources to watercourses. The model allows scenario analysis of the likely impact of flow path mitigation on diffuse nutrient loads.

Hortonian and Variable Source Area Modeling in Urbanizing Basins

The conventional hydrological model QualHYMO, which uses infiltration excess overland flow as the primary mechanism for runoff generation, is compared with a variable source area model that was modified for use on urbanizing watersheds. The modified variable source area model is known as TOPURBAN, as it uses TOPMODEL concepts to generate saturation excess overland flow. TOPURBAN proved to provide better modeling efficiency than QualHYMO in four continuous modeling tests, and slightly better efficiency in two continuous modeling tests. QualHYMO was found to produce large overpredictions due to its representation of urban areas, and the assumption of the entire rural area contributing to flow when rural losses were exceeded. TOPURBAN slightly underpredicted peak flows, but other hydrograph characteristics were modeled well. TOPURBAN outperformed QualHYMO in applications to two single events with similar antecedent moisture conditions. TOPURBAN is considered by the writers to be a good predictor of flow rate...

Variable source area modelling in urbanizing watersheds

A variable source area model called TOPMODEL was modified and tested for its applicability on urbanizing watersheds. The model was modified to consider urban land uses by altering the topographic index and the mechanism of surface runoff generation. A Geographic Information System was utilized to delineate the catchment, determine the urban areas and produce Digital Elevation Models. The model was applied to a small catchment of approximately 8 km 2 in southern Ontario that is characterized by mild slopes, well-draining soils and a semi-humid climate. Testing was conducted using a partially revised model with four calibration parameters (TOPURBAN v. 1) applied to three separate time periods; and a fully revised model with five calibration parameters (TOPURBAN v. 2) applied to six time periods. The model performed well with calibrated model efficiencies of greater than 70%. Verification efficiencies ranged from 20 to 70%. TOPURBAN v. 2 increased Nash and Sutcliffe efficiency in comparison to v. 1 by anywhere from 2 to 8% as it accounted for storage in the urban areas. This model is recommended for urbanizing catchments of small to moderate size. Some calibrated parameter interaction was observed between parameters dealing with the urban areas and parameters dealing with the natural areas.

Grid-resolution effects on a model for integrating urban and rural areas

The impact of grid-cell size on calibrated parameters and on the performance of a variable source area model intended for urbanizing catchments is studied in this research. The model uses TOPMODEL concepts that were modified to consider urban areas in both the topographic index and the mechanism of surface runoff generation. The revised model known as TOPURBAN, was applied to a small catchment of roughly 8 km2 in southern Ontario. Ten different grid-cell sizes ranging from 10 m to 100 m were selected to study scale effects in this catchment with mild to moderate relief, on three separate time periods. The model performed adequately with calibration efficiencies for all three time periods in the range of 0\65 to 0\85. The verification efficiencies were not as high and ranged from 0\4 to 0\6. Larger cell sizes produced higher averages of topographic index, and this resulted in larger calibrated transmissivities. The most important parameter in determining the quantity of urban runoff was slightly affected by grid resolution. During the calibration process, this parameter was also found to interact with important parameters that dealt primarily with rural runoff generation. As cell size increased, contributions from urban areas increased and overland flow contributions from rural areas decreased. Results showed that in this integrated model of urban and rural areas, predicted processes based on calibrated parameters were dependent on grid resolution. Calibration of internal state variables is recommended to draw conclusions on the influences between urban and rural areas on the overall flow. Copyright © 2000 John Wiley & Sons, Ltd.

The suburban energy balance: Methodological considerations and results for a mid‐latitude west coast city under winter and spring conditions

AbstractPrevious measurements of the urban energy balance primarily have been conducted in summertime. This paper reports the first extended set of winter‐spring‐time energy balance measurements for a city. The study was conducted in a suburb of Vancouver, British Columbia, from January to June 1987. It included hourly measurements of net all‐wave radiation, sensible heat flux and the Bowen ratio. The anthropogenic and storage heat fluxes were modelled. A dynamic source area model was employed to ensure the modelled parameters were consistent spatially with the measured turbulent fluxes. The winter‐spring urban energy balances observed in this study are different to those reported for summertime conditions at the same site. The fluxes for the entire period are not symmetrical about solar noon. Hence earlier interpretations possibly should be modified. Apart from this feature the spring season balances are similar to those reported for the summertime in terms of relative importance of individual fluxes. The wintertime energy balance appears to be different to that of spring and summer. The most noticeable feature is the increased importance of the latent heat flux, which on average is the largest output flux in the balance. A secondary, more expected feature, is the increased importance of anthropogenic heat flux as an input in winter.

A model to estimate the source area contributing to turbulent exchange in the surface layer over patchy terrain

AbstractThe characteristics of turbulence in the surface layer are well understood over spatially homogeneous and smooth surfaces. Current theoretical knowledge is based on measurements over such ‘ideal’, flat and homogeneous surfaces. Over heterogeneous surfaces of a patchy nature (e.g. urban areas, mixed agricultural crops, forest etc.) turbulence is subject to considerable spatial variability over a wide range of scales.A ‘source area’ is defined as the portion of the upstream surface containing the effective sources and sinks contributing to the turbulent exchange processes at a given point in the surface layer. It is noted that the term ‘source area’ refers to sources and sinks on the surface only and does not consider production or dissipation within the atmosphere. the contributions of surface elements are treated as ‘plumes’ of heat or vapour or momentum‐deficiency. A small‐perturbation approach to diffusion theory and a plume‐diffusion model are used in a numerical source‐area model (SAM) to estimate this region, depending on meteorological scaling parameters and the reference location. This model identifies a ‘maximum effect source location’ and the upwind, downwind and lateral dimensions of regions containing various levels of the total contributing effect. It accounts for the different source weight of each point on the surface, depending on its position relative to the reference location. Although the source area is not directly measurable, the results of SAM compare favourably with observed effects of changing source areas.A sensitivity test of SAM results and non‐linear regression leads to a set of simple equations (mini‐SAM) approximating SAM. This short‐cut model provides easily obtainable estimates of the source‐area dimensions and the relative importance of surface elements for a given measurement of turbulent exchange.

Snowmelt runoff modeling in a balsam fir forest with a variable source area simulator (VSAS2)

The variable source area model of storm flow generation VSAS2 has been adapted to simulate snowmelt runoff in the Lac Laflamme forested basin, 80 km north of Quebec City. The model has been adapted to accept different water inputs according to topography, to factor the effect of lake water storage in the discharge hydrograph and to process 3 months of hourly data. To ensure convergence of the mathematical solution, the explicit form of flow equations included in VSAS2 has been transformed to use an iterative approach. Lysimeter measurements as well as outputs from the snowmelt temperature index model SNOW‐17 were used as input data in the simulation. Results showed that low flows in early spring were well reproduced by the physically based model. However, all seasonal (1985, 1986 and 1987) peak flows were underestimated when all water input was considered to infiltrate. Observations on the site showed that the natural topographical drainage network was augmented in the spring by superficial concrete frost, pipe throughflow at the organic‐mineral soil interface and snowpack basal ice layers. It was therefore necessary to use an infiltrability index to improve the model. Because it was closely related to the development of an impervious layer at the soil surface, the relative proportion of bare ground areas on the basin was also related to the rising of streamflow hydrographs. Thus values of snow cover areal extent were taken from SNOW‐17 outputs and used as an index to the prevailing conditions of soil infiltrability on the basin. Results from VS AS2 were greatly improved, supporting the hypothesis of an important surface flow contribution during late snowmelt. The study underlined the necessity of further field investigations on the dynamics of infiltration processes into frozen soil.

The relationship of catchment topography and soil hydraulic characteristics to lake alkalinity in the northeastern United States

We undertook the task of determining whether base flow alkalinity of surface waters in the northeastern United States is related to indices of soil contact time and flow path partitioning that are derived from topographic and soils information. The influence of topography and soils on catchment hydrology has been incorporated previously in the variable source area model TOPMODEL as the relative frequency distribution of ln (a/Kb tan B), where ln is the Naperian logarithm, “a” is the area drained per unit contour, K is the saturated hydraulic conductivity, b is the soil depth, and tan B is the slope. Using digital elevation and soil survey data, we calculated the ln (a/Kb tan B) distribution for 145 catchments. Indices of flow path partitioning and soil contact time were derived from the ln (a/Kb tan B) distributions and compared to measurements of alkalinity in lakes to which the catchments drain. We found that alkalinity was, in general, positively correlated with the index of soil contact time, whereas the correlation between alkalinity and the flow path partitioning index was weak at best. A portion of the correlation between the soil contact time index and alkalinity was attributable to covariation with soil base saturation and cation exchange capacity, while another portion was found to be independent of these factors. Although our results indicate that catchments with long soil contact time indices are most likely to produce high alkalinity base flow, a sensitivity analysis of TOPMODEL suggests that surface waters of these same watersheds may be susceptible to alkalinity depressions during storm events, due to the role of flow paths.

A practical exercise to demonstrate the variable source area model

Abstract A practical exercise is described which allows students to measure the spatial variation of runoff production within a low‐order drainage basin. Dilution gauging techniques are used to measure stream discharge. These discharge data may then be used to provide evidence of the spatial pattern of sediment and solute delivery within the basin. A full description and evaluation of the practical is provided. Details of the gauging measurements are given in the appendix.

Morphology and geochemistry of different pyrite types from the Upper Witwatersrand System of the Klerksdorp Goldfield, South Africa

The morphology of pyrites from the Proterozoic, auriferous and uraniferous conglomerates of the Upper Witwatersrand System of the Klerksdorp Goldfield (South Africa) was studied by means of scanning electron microscopy (SEM). The pyrite particles were recovered by hydrofluoric acid leaching, thus making a three-dimensional SEM examination possible. According to morphological criteria the pyrites were classified into three types. Trace-element analysis by atomic absorption spetrophotometry (Au, Co, Ni, Cu, Zn, Pb, Mn, As) and the statistical evaluation of the results confirmed the morphological classification: Type 1: Authigenic, idiomorphic to hypidiomorphic pyrites or pyrite accumulations, which were formed in the conglomerates during diagenesis or metamorphism. Type 2: Allogenic, rounded, compact pyrites. This type was eroded from primary deposits in the hinterland of the Witwatersrand basin and deposited with the Witwatersrand sediments. It shows the closest trace-element affinity to pyrites from the Barberton Mountain Land, the source area model for the Witwatersrand sediments. The recognition of this pyrite type from the Klerksdorp Goldfield is in agreement with observations on detrital compact pyrites described from other goldfields of the Witwatersrand. Type 3: Allogenic, rounded, porous pyrites. These were formed from pyritic muds and iron sulfide gels existing on the surface of the alluvial fan, and later were reworked as mud balls or fragments and deposited with the conglomerates. Indentations with radial fracture patterns point to transport partly in a plastic state. The occurrence of colloform pyrites among this type supports the postulation of pyritic muds or iron sulfide gels. Only in this type of pyrite various inclusions such as gold, quartz, silicates, brannerite, copper- and titanium-bearing minerals were found. It is suggested that these inclusions were trapped as dust-like particles in the pyritic muds or iron sulfide gels on the surface of the alluvial fan. Only the presence of the allogenic, porous pyrites could be correlated with high gold values in the conglomerates.

A variable source area model of the rainfall‐runoff process based on the Watershed Stream Network

A model of the dynamic contributing area during a storm is formulated in terms of the history of precipitation in excess of B horizon permeability. The spatial dynamic contributing area along the main stream is obtained under the assumptions that the velocity of flow along the stream network is uniform, the drainage density is a constant within a given watershed, and the first‐order streams are uniformly distributed in the basin. The runoff from the dynamic contributing area is then routed through the synthesized stream network to obtain the direct runoff at the basin outlet by making use of a method based on the linearized Saint Venant equations. The model has been tested in several watersheds in the central United States.

The Hydrologic Response of The Eaton River Basin, Quebec

This paper reports a parametric study of rainfall–runoff relations for 38 storms in the Eaton basin, southeastern Quebec, between 1950 and 1966. In addition to storm rainfall amounts, water table levels in the vicinity of the channel network, as indicated by baseflow prior to storms, appear to be very important in controlling the amount of response of the basin in different storms. Storm runoff is viewed as the product of direct interception by, and subsurface seepage into, expanded surface water systems in the valley floor areas of the basin. This is in agreement with the variable (partial) source area model developed over the last ten years by a number of hydrologists as an alternative to the Horton theory of runoff production.