^{*}

^{†}

Current Address: Department of Remote Sensing, Institute of Geography, University of Wuerzburg, Campus Hubland Nord -86-, D-97074 Wuerzburg, Germany.

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

This study highlights the possibilities and constraints of determining instantaneous spatial surface radiation and land heat fluxes from satellite images in a heterogeneous urban area and its agricultural and natural surroundings. Net radiation was determined using ASTER satellite data and MODTRAN radiative transfer calculations. The soil heat flux was estimated with two empirical methods using radiative terms and vegetation indices. The turbulent heat fluxes finally were determined with the LUMPS (Local-Scale Urban Meteorological Parameterization Scheme) and the ARM (Aerodynamic Resistance Method) method. Results were compared to

The surface energy budget is an important term in the climatological system. It determines how the energy received from solar irradiation is distributed to other climatological terms. For example, areas with a high albedo reflect back a high amount of the solar irradiation, following that, the available energy for heating the soil and the near-surface air layers or evaporating water from the surface is low. Despite this, a change of the surface albedo has a direct impact on the radiative forcing and therefore on the microclimate. Such changes can arise by natural processes or through human impact. The construction of cities is an example of such a human interference. Besides the albedo, other surface properties like the heat storage capacity or the soil water storage capacity are also altered in cities, leading to different magnitudes and ratios of surface fluxes. In particular, megacities came to the notice of recent national and international political and social attention. More than half of the world’s population lives now in urban regions and megacities are a consequence of this migration process. Through the increased spatial extent of such urban regions, megacities become relevant for the local and even regional climate [

In the last decade, many studies have tried to estimate land surface fluxes from remote sensing images, e.g., [

The goal of this study is to show the possibilities to determine the whole instantaneous energy budget from ASTER satellite images for single dates of a remote area featuring very contrasting surface covers, using as few

From literature, there are three distinct groups of methods for the estimation of instantaneous turbulent heat fluxes. They can be summarized as (a) Bulk transfer approaches, (b) the Local-Scale Urban Meteorological Parameterization Scheme (LUMPS) scheme, and (c) extreme pixel approaches. These three groups, which all need a measurement channel in the thermal infrared, will be touched on in the following.

The bulk transfer approach uses remotely-sensed surface temperatures, together with an estimation of air temperature, net radiation, and ground heat flux to derive turbulent heat fluxes. The approach focuses on the determination of the resistance to heat transfer r_{h}. The estimation of the single terms is sometimes problematic. For example, the term r_{h} is a function of surface roughness, wind speed, and stability [

The LUMPS approach, introduced by [

The third group of methods, the extreme pixel approaches, uses extreme wet and dry pixels rendered either by manual setting or by the relation of surface temperature and surface albedo to find the partition of turbulent heat fluxes for each pixel. These methods originate in the SEBI (Surface Energy Balance Index) formulation proposed by [

Please refer to [

To compare the results of the LUMPS and ARM methods against field values, a measurement campaign was conducted from October 2007 to February 2008 in Greater Cairo. All relevant variables were continuously measured at three stations, each representing a major land cover class: ‘urban’, ‘suburban agricultural’ and ‘suburban desert’. Further details and results from this campaign are described in [

The study area is Greater Cairo, the largest city in Egypt and on the African continent. Greater Cairo is a megacity, which administratively belongs to three different units: the governorates of Cairo, Giza and Qalyubiyya. For this historical division of the contiguous agglomeration of the megacity, and due to many unregistered residents, cited inhabitant numbers may differ considerably. As a whole, the population can be estimated to about 20 million inhabitants [

The main remote sensing data source was ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer), an optical imager on the TERRA satellite of NASA. It crosses the equator at about 10:30 local time. The spectral resolution ranges from the very visible to the thermal infrared with a spatial resolution from 15 m in the visible to 90 m in the thermal infrared. ASTER has a swath width of 60 km and its revisit time is 16 days. These features make ASTER an optimal candidate for medium-scale landscape analyses. A key question of this paper is how this ASTER data can be used for energy balance studies in urban regions.

Atmospheric correction of the ASTER data was performed using the radiative transfer model MODTRAN with midday radiosonde ascents from Helwan, south of Cairo, as input atmosphere. After [

Two versions of atmospheric correction are used in this study: a ‘best guess’ version, using the MODTRAN aerosol setting ‘urban, visibility 5 km’, and a ‘best fit’ version, using the aerosol setting ‘rural, visibility 23 km’. The second version produced the better matching of the broadband albedo with

Unfortunately, the ASTER SWIR instrument suffers from thermal anomalies from December 2008. Therefore, the SWIR data from 24 December and 2 January could not be used in this study. It mainly affected the estimation of the broadband albedo. All scenes had more or less cloud contaminations. Cloud areas were first detected using an automated cloud-detection algorithm. As the algorithm was not able to detect all areas where strong haze occurred, additional manual edition was necessary. The cloudy areas were not used in any of the following analyses.

Additionally, a scene of ASAR (Advanced Synthetic Aperture Radar), an imaging microwave radar operating at C-band, was used in this study. The scene was acquired in the ASAR image mode, where only one of seven predetermined swaths is sensed. A geolocated level 1B product with polarization set to ‘VV’ was chosen. Spatial resolution of the delivered product was 12.5 m. Further, the SRTM (Shuttle Radar Topography Mission) digital elevation model of the region was downloaded. Both the ASAR and the SRTM were georeferenced to the VNIR ASTER images using manual chosen pass points. Through this process, the spatial resolution was also adjusted to the VNIR ASTER resolution (15 m).

Flux measurements using the eddy covariance technique frequently suffer from a closure gap in the energy balance (e.g., [

Another constraint of the eddy covariance technique is that fluxes are average values of a certain time period (30 min in the CAPAC campaign), while satellite data are instantaneous measurements. Therefore, during the averaging period, considerable changes in the radiation situation might occur, probably influencing the derivation of these fluxes. Such changes are not incorporated in the satellite measurement, surely leading to a certain mismatch when comparing products from the two approaches.

Finally, it should be mentioned that the anthropogenic heat flux cannot be measured separately and is included in the sensible and the ground heat flux.

Not all stations (‘Cairo University’, ‘Bahteem’, and ‘10^{th} Ramadan’) were covered by all scenes. The following dates of ASTER data were available during the campaign in Cairo. An X in

The net radiation Q^{*} [W·m^{−2}] is given as
^{−2}], ^{−2}], and ^{−2}]. In the following, all terms will be explained separately.

To convert the spectral reflectances ρ of ASTER obtained from the atmospheric correction algorithm to broadband albedos, an empirical equation was used, which was gained from a multiple regression approach similar to [

In case of the ASTER scenes from 24 December 2007 and 01 February 2008, only the VNIR bands were available due to a temperature anomaly in the detector. Therefore, another equation was obtained for these dates. The resulting empirical regression equations are listed in the annex.

For the outgoing long wave emission L_{↑}, the atmospheric corrected TOA (Top Of the Atmosphere) radiances using the ‘best guess’ option for the atmospheric correction were converted to brightness temperatures using the Planck-function. As the Planck-function is only valid for a single band wave number, the correction of the least-square-fit method described in [_{bi}) were then converted to broadband emissivities (ε), using empirical regression equations for each land use, similar to the albedo approach. The equations for the different land use classes are also in the annex.

Incoming broadband irradiation K_{↓} was estimated using MODTRAN runs over the short wave range from 0.25 to 4 μm. For the option ‘best guess’, the same MODTRAN settings were used, as for the atmospheric correction of the band radiances in the ‘best guess’ mode. For the option ‘best fit’ however, the _{↓} values from the CAPAC campaign [_{↓} values. The spatial solar irradiation K_{↓} is given as the sum of beam irradiation, diffuse irradiation, and irradiation reflected from the environment and is calculated in dependence on the sky view factor which was derived from the SRTM DEM [

Incoming long wave radiation L_{↓} was also estimated using the ‘best guess’ option in MODTRAN. Yet, no ‘best fit’ option was introduced to the long wave fluxes.

The ground heat flux Q_{s} [W·m^{−2}] is a function of the available energy on the surface and the layers beneath and the thermal properties of the soil. Thermal properties are dependent on soil moisture and porosity and therefore only constant at sealed surfaces. Whilst the estimated Q* stands for the available energy, it is more difficult to describe the thermal properties of the ground. Common approaches found in literature are using different vegetation indices for this purpose [

Apart from this approach, a new formula was derived using linear regression with a set of _{s} (07:00–16:00) from the period from 20 November 2007 to 20 February 2008 were used. The data were filtered for sunny hours by comparing actual net radiation to an adapted sine wave. The daily curve of Q_{s} features a time offset towards the curve of Q* of about one hour (see _{s}, measuring the flux a few centimeters underground. Therefore, the whole time series of the latter parameter was shifted backwards one hour for the regression calculations (Q*_{h−1}). The NDVI then explains the differences between the stations, similar to the ‘Parlow/urban’ approach. The first term in equation 9 explains the variation of the land use and was derived specifically for the late morning hours. The second term describes the relation between Q* and Q_{s} and is valid for the whole day.
_{s} was not measured at the urban station. Therefore, it had to be deduced from the balance of Q* and the turbulent heat fluxes. However, for surfaces which were not perfectly homogeneous, the energy balance is not closed and a considerable unexplained residual remains. This residual was roughly estimated for the urban station using the residuals from the agricultural and the desert station. Then Q_{s} was derived as balance from Q*, the turbulent heat fluxes and the estimated residual.

Besides Q*, other variables like α or ε were tested for their feasibility in describing Q_{s}. However, none of these variables was able to improve the regression coefficients.

LUMPS stands for the Local-Scale Urban Meteorological Parameterization Scheme and was developed to calculate turbulent fluxes using standard meteorological measurements and two semi-empirical parameters describing the surface cover. Its origin is a simplified Penman-Monteith approach, incorporating the Priestley–Taylor coefficient for extensive wet surfaces and extending it to non-saturated surfaces [_{H}, Q_{LE}) and the available energy (Q* − Q_{s}), β stands for the uncorrelated part [

An alternative method to estimate the sensible heat flux is the bulk transfer equation,
_{air} is the density of air [kg·m^{−3}], C_{p} the specific heat of air at constant pressure [J·kg^{−1}·K^{−1}], T_{s} is the surface temperature [°K] calculated from the ASTER TIR data and T_{a} is the air temperature [°K]. r_{h} is the aerodynamic resistance for heat [s·m^{−1}] [_{LE} is then the residual of the available energy and Q_{H}. Spatial T_{a} had to be estimated and was deduced using empirical regression equations with T_{s} and wind speed obtained from the CAPAC campaign data. The equations are given in the

The aerodynamic resistance r_{h} can be determined with an approach using the roughness length, stability correction functions for momentum and heat, and the friction velocity [_{h} and the radar backscattering coefficient σ^{0} of the ASAR image from 2 January 2008.

The radar image was smoothed with a 13 × 13 filter to remove speckle and other disturbing effects before serving as input in the regression calculation, together with the wind speed wnd_spd [m·s^{−1}]. The resulting equation is

Eddy flux towers measure fluxes originating from an extended upwind source area of the tower. The spatial extent of the source area depends on the measuring height, the roughness of the surface, and the stability of the boundary layer. In the CAPAC campaign, considerable directionality was found in the turbulent flux data, especially at the agricultural station ‘Bahteem’ [

The presentation of the results follows two strategies. First, the calculated parameters from the ASTER data are compared to the

In a second step, the spatial variations in the image are discussed on the basis of what is expected and realistic. The basis for this discussion are the general land use classes ‘urban’, ‘agriculture’ and ‘desert’.

The calculated radiation fluxes from the ‘best guess‘ and the ‘best fit‘ option were compared to the

For the urban and the agricultural station, three overflights could be used; the desert station had four scenes available for comparison. The MADs of these 10 value pairs were calculated and are listed in ^{−2} could be improved significantly by using the ‘best fit’ option, reducing the MAD to only 10.1 W·m^{−2}. The two long wave terms both showed good agreement in the ‘best guess’ case, therefore no ‘best fit’ option was introduced. Finally, the net radiation could be determined with 11.6% accuracy in the ‘best guess’ option, and with 6.9% in the ‘best fit’ option. As the ‘best fit’ option is fitted to the measurement values, this comparison is of course not independent. Anyhow, the ‘best guess’ version can be interpreted as an error measure for other pixels not included in this comparison.

The

A main constraint in the modeling of the irradiation was the limited accuracy of the used DEM. The DEM had a spatial resolution of 3 arcsecond (≈90 m), but could not resolve exactly the geomorphologic features occurring in the desert, such as wadi systems. Further, the modeling of the irradiance reflected from opposed slopes is simply parameterized using the neighboring pixel’s reflectance and therefore might be underestimated. Hence, areas of massive over- and underestimation of the incoming spectral irradiance were present in some areas of the desert, finally resulting in wrong albedo values. Also, radar data exhibit increased scattering over rough surfaces. Therefore, the SRTM data over urban areas showed some irregularities. To account for this, the slope was set to zero over urban areas. A further constraint is given by the fact that solar irradiation was modeled assuming the urban surface to be flat; for example, no enhanced reflections from sun-facing walls and sloped roofs or diminishing effects of shadows were considered. In urban areas, this assumption can lead to considerable errors, as was shown in [

A similar distribution is found in all scenes; however, in some scenes, the net radiation of the urban areas almost equaled the net radiation of the agricultural areas. The main reason for this difference is the albedo. For example, the difference between the mean urban and mean agricultural albedo of the scene (b) from 01 December 2007 is only 0.7%, while in the scene (b) from 24 December 2007, which covers a very similar sector, it is 4.1%. Even though the difference between the mean values seems to be small, there is a resultant effect on the spatial pattern. The urban net radiation of the scene (b) from 01 December 2007 is only 9.1 W·m^{−2} lower than the agricultural net radiation. In the case of the scene (b) from 24 December 2007, it is 30.3 W·m^{−2} lower.

Q_{s} was derived using the ‘Parlow/urban’ and the new ‘Frey/NDVI’ approaches. It was compared to half hour averages of Q_{s} from the measurement campaign. The option ‘best guess’ and the option ‘best fit’ were used as input in the comparison through the net radiation. Generally, the option ‘best fit’ performed slightly better than the option ‘best guess’, although the MAD of ‘best fit’ was only few percent higher than ‘best guess’. The best agreement showed the ‘Parlow/urban’ approach. There the MAD for the option ‘best fit’ was 18.9 % of mean Q_{s}. The new approach performed similarly well. _{s}.

Spatial analysis showed that both approaches were in agreement with the general assumed spatial pattern with agricultural pixels having the lowest Q_{s} and urban pixels featuring the highest values. The desert pixels ranged somewhere in between. However, the ‘Parlow/urban’ approach showed another pattern in 3 scenes: here the means of the urban and the means of the desert pixels were almost similar.

Q_{H} and Q_{LE} estimated with the LUMPS scheme were calculated using both the ‘Parlow/urban’ and the ‘Frey/NDVI’ approaches for Q_{s}. At the urban station, three value pairs (a pair consists of one

The parameters from [_{H} and Q_{LE} at the desert station. Taking the ‘Parlow/urban’ method for Q_{s} and using the ‘best fit’ option for Q*, the MAD of Q_{H} and Q_{LE} was 13.4 W·m^{−2}, and 16.2 W·m^{−2} respectively, in case no footprint model was used. The parameters retrieved from the campaign in Cairo produced similar good results for this station. This good fit is mainly due to the simple environment at the desert station, facilitating the model development. At the urban and the agricultural stations, higher MADs of 40.0 W·m^{−2} and 95.2 W·m^{−2} for Q_{H} and 41.3 W·m^{−2} and 116.6 W·m^{−2} for Q_{LE} were observed for the same setting taking the parameters from [

Of course, the LUMPS parameters derived from the measurement data performed better for both the urban and the agricultural station. MAD of Q_{H} of the urban station was 26.6 W·m^{−2}, of the agricultural station 3.5 W·m^{−2} and of the desert station 12.0 W·m^{−2} in case no footprint model was used. The respective values of Q_{LE} are 18.3 W·m^{−2}, 24.9 W·m^{−2}, and 15.1 W·m^{−2} (compare

The MAD mostly increased, not when using the ‘best fit’ option, but rather the ‘best guess’ option for the net radiation input in the calculations. The appropriate MADs for the urban, the agricultural and the desert station also using the ‘Parlow/urban’ Q_{s} were then 37.0 W·m^{−2}, 5.2 W·m^{−2} and 20.0 W·m^{−2} for Q_{H} and 20.5 W·m^{−2}, 32.1 W·m^{−2}, and 14.8 W·m^{−2} for Q_{LE}. The MAD also increased in almost all cases, taking the parameters from [

MADs for Q_{H} and Q_{LE} change only at the agricultural station, when using the ‘Frey/NDVI’ approach for Q_{s}. There, the MAD of Q_{LE} decreases to 16.2 W·m^{−2}, and MAD of Q_{H} increases to 14.1 W·m^{−2}, both for the ‘best fit’ option. At the two other stations, the MADs remained almost the same.

From the results of the LUMPS method, we can see that it is fairly reasonable to model turbulent heat fluxes in desert-like environments from values in the literature, but it is more critical to do so in urban or agricultural environments.

To evaluate the performance of the LUMPS approach further, the KM footprint model was applied to the results of the approach. Due to cloudiness, not all values could be used in the footprint analyses. There was a limitation in the calculation that at least 70% of the accumulated flux footprint must be cloud free, otherwise the result was invalid. Unfortunately, the pixel of the desert station of the first ASTER scene was set to invalid due to cloud cover. The use of the footprint model only partly improved the results. In most cases, the results were even worse. The Q_{H} MAD values only improved significantly at the agricultural station, and in some cases, the LUMPS parameters from literature were used. Q_{LE} sometimes improved, other times not. Overall, the effect of the footprint models was ambiguous. _{H} and Q_{LE} for all calculated combinations.

Spatial analysis of the LUMPS heat fluxes showed that the different approaches produced fairly different patterns. Following [_{LE} which were lower than the desert Q_{LE}. _{LE} modeled using the ‘Parlow/urban’ Q_{s} and the newly-retrieved parameters for the LUMPS parameters.

Q_{H} however, did not always follow this order. On one day for example, 22 November 2007, mean agricultural Q_{H} was higher than mean urban or mean desert Q_{H}. In _{LE} was modeled quite well. This is attributed to the fact that the LUMPS parameters α and β deducted from the _{LE}. Q_{H} in

Looking at the Bowen ratio β (=Q_{H}/Q_{LE}), the desert showed the highest β values, the urban areas slightly lower values and the agricultural areas the lowest β. The MAD of the desert β thereby was found to be 5 < β < 7, agricultural areas featured 0.5 < β < 3 and urban areas 1 < β < 3. However, using the parameters from the literature, they rendered extremely high urban β (10 < β < 28) and also very high agricultural values (β ≈ 3).

Q_{LE} estimated with the ARM method was calculated with the ‘Parlow/urban’ Q_{s} only, as no significant influence was found from taking either the ‘Parlow/urban’ or the ‘Frey/NDVI’ Q_{S} in the analysis of the LUMPS results. Generally, MAD of Q_{H} and Q_{LE} from the ARM method were higher than the MAD of the LUMPS approach. Especially at the desert station, the agreement worsened. Only the agricultural value matched better with the ARM method. MAD of Q_{H} for the urban, the agricultural and the desert station were 49.1 W·m^{−2}, 1.4 W·m^{−2} and 25.0 W·m^{−2} for the ‘best^{−}fit’ option. The MAD of Q_{LE} for the same stations was 74.8 W·m^{−2}, 27.7 W·m^{−2} and 25.4 W·m^{−2}. At the urban, station the ‘best guess’ option of Q_{LE} performed better than the ‘best fit’ option (65.3 W·m^{−2}). However, at the agricultural and the desert station, the ‘best fit’ approach performed better.

Spatial analysis of the ARM heat fluxes followed the same rules as in the LUMPS analysis. Q_{LE} was modeled correctly, with the agricultural Q_{LE} the highest, the desert Q_{LE} the lowest and the urban Q_{LE} somewhere in between. Also, Q_{H} showed a reasonable distribution. _{H} and Q_{LE} for the ‘best fit’ option and the ‘Parlow/urban’ Q_{s}.

The analysis of the Bowen ratios β also showed that most methods assigned the desert β highest values, the urban areas slightly lower β and the agricultural areas the lowest. However, in some cases the desert had a negative latent heat flux, resulting in negative β values.

The findings of this study highlight the possibilities and difficulties of instantaneous flux determination from remote sensing images. ASTER images are well suited for this task concerning their spatial and spectral resolution. The temporal resolution, however, is insufficient for a regular flux determination from space.

This study showed that it is possible to determine turbulent heat fluxes from space within a good accuracy range. The differences found between remote sensing and

There is the error propagation from input variables, which was mentioned by [^{−2} (scene (a) of 22 November 2007, ‘best guess’) due to an inappropriate value of a MISR AOD product pixel. Q* then was underestimated 111.2 W·m^{−2}. In the LUMPS approach this produced a difference to the ‘best fit’ option in Q_{H} of 31.1 W·m^{−2} taking the campaign retrieved parameters and the Q_{s} of ‘Parlow/urban’. The difference in Q_{LE} with the same input is only 4.7 W·m^{−2}. Using the ARM approach, the difference between this ‘best guess’ option and the ‘best fit’ option is 35.7 W·m^{−2} for Q_{LE}. Dealing with such magnitudes, it is difficult to decide whether a spatial pattern is mainly governed by land use or due to incorrect atmospheric correction.

The ground heat flux is an important input variable and also determines the accuracy of the subsequently calculated heat fluxes. Differences found between the remote sensing and the

The second concern in determining turbulent heat fluxes is the model uncertainty itself. Especially in heterogeneous environments, the development of a good model is important. For instance, the LUMPS method is using two empirical parameters which are dependent on the environment. It is a great challenge to find the right values for each pixel in such a fast changing landscape, especially as

In the ARM method, both concerns can be found in the determination of the aerodynamic resistance for heat, which is dependent on surface roughness and on the conditions of convection and winds. An improper estimation of this variable will lead to a weak determination of heat fluxes. Additionally, the spatially distributed air temperature has to be estimated in the ARM method—A step which is crucial for flux determination accuracy.

Bare soil and plant foliage temperatures contribute both to radiometric surface temperatures and contribute to the turbulent transport of sensible heat [

The discussion so far about flux determination accuracy neglects the problem of the imprecise determination of the turbulent fluxes by eddy covariance measurements. In inhomogeneous areas especially, the onsite flux determination is difficult, but also at our desert station, the measured energy balance had to be closed by force. Before closing, midday ensemble average of the residual term from the desert station was nearly 60 W·m^{−2}; at the agricultural station, it almost reached 150 W·m^{−2}. Similar residuals were found by [

The estimation of the radiation and energy balance from satellite images strongly depends on a successful atmospheric correction. Especially in areas where the aerosol content of the troposphere is not constant (for example due to air pollution as in our research area), the atmospheric correction is a crucial task. In this research, two versions of atmospheric correction were used: ‘best guess’ and ‘best fit’, with ‘best fit’ being the version that produced albedos that fit the ground measurements better than the ‘best guess’ version. The albedo is estimated with a 14.8% accuracy in the ‘best guess’ scenario. Short wave irradiation was estimated with 7.4%, long wave emission with 2.0%, incoming long wave radiation with 6.5%, and finally the net radiation with 11.6% accuracy. The ‘best fit’ case improved these values considerably, e.g., the net radiation was estimated in the ‘best fit’ case with 6.9% accuracy. Considering the accuracy of the

The ground heat flux could be modeled satisfactorily using two different approaches when comparing the values to 30-minute averages of ^{−2} in all cases. The MAD (mean absolute difference) is 15.5 W·m^{−2} for the ‘Parlow/urban’ method and 17.5 W·m^{−2} for the ‘Frey/NDVI’ method using the ‘best fit’ option. Looking at the spatial distribution, both approaches rendered proper values.

All in all, five possible methodological combinations were used to calculate Q_{H} and Q_{LE} with the LUMPS approach. Combinations included the ‘best guess’ and the ‘best fit’ option of Q*, different approaches for α and β, and two sources for the ground heat flux. Overall, MAD (including all combinations) of Q_{H} of the urban station was 36 W·m^{−2}, which is 19% of the mean ^{−2} (34%), and at the desert station, it was 17 W·m^{−2} (17%). The respective values for Q_{LE} were 28 W·m^{−2} (57%), 62 W·m^{−2} (34%) and 16 W·m^{−2−}(61%). The best combination consisted of the 'best fit' case for the atmospheric correction, the ‘Parlow/urban’ approach for the ground heat flux and the newly-derived LUMPS parameters. In this case, the MADs for Q_{H} were 27 W·m^{−2} (14%), 4 W·m^{−2} (3%), and 12 W·m^{−2} (8%) and the MADs for Q_{LE} were 18 W·m^{−2} (38%), 25 W·m^{−2} (14%), and 15 W·m^{−2} (60%).

The desert station showed the best absolute results due to its simple and homogeneous environment and general very low latent heat fluxes. The agricultural station, on the contrary, showed the highest deviations, which probably resulted from the high fragmentation of the landscape. The urban station was somewhere in between. Considering the uncertainty of the

The analysis of the spatial distribution of the LUMPS fluxes revealed that Q_{LE} was modeled according to our expectations; however, Q_{H} showed some irregularities. Summarizing the LUMPS results, we conclude that the estimation of the turbulent heat fluxes with literature values is only applicable when the environment is fairly simple, like our desert example. As soon as the environment becomes more complex, the determination is more difficult.

The ARM approach was calculated with the two combinations for the atmospheric correction - ‘best guess’ and ‘best fit’ options of Q*. MAD of Q_{H} of the urban station was 49 W·m^{−2}, which is 26% of the mean ^{−2} (1%) and at the desert station, it was 25 W·m^{−2} (16%). The respective values for Q_{LE} were 70 W·m^{−2} (145%), 37 W·m^{−2} (20%) and 35 W·m^{−2} (211%). Generally, similar results to the LUMPS analysis were found. ‘Best fit’ worked better than the ‘best guess’ option. The spatial analysis showed that the ARM approaches were able to reproduce meaningful spatially-distributed fluxes in contrary to the LUMPS approach.

The application of the footprint model increased the MAD in most cases for both the LUMPS and the ARM method. It is therefore not encouraged to use such models when working with high uncertainties.

This study showed that it is reasonable to calculate the energy balance using spaceborne data when sufficient

This work was supported by the Swiss National Science Foundation (grant number 200020-120080/1).

The regression equations for the broadband albedo are:

The subscripts b1–b9 denotes the respective bands of the ASTER scenes. The equations for the broadband emissivity for the different land use classes are:

Desert:

Vegetation:

Water:

Urban:

The regression equations for estimation of spatial air temperature are
_{spd} being the wind speed at the respective land use.

Q* of one hour before the overflight (Q*_{h−1}) can be calculated from Q*_{h}, assuming that Q* follows the above-mentioned idealized sine wave. In the morning, the wave starts at the point, when Q* becomes positive (sine = 0). It then grows to the maximum (sine = 1) at the point of time when Q* has its maximum, to decrease to sine = 0 again in the evening, when Q* becomes negative. Q*_{h−1} is then

Γ values for the calculation of the sinus curve.

07:00 | 0.000 | 12:00 | 1.396 |

07:30 | 0.175 | 12:30 | 1.222 |

08:00 | 0.349 | 13:00 | 1.047 |

08:30 | 0.524 | 13:30 | 0.873 |

09:00 | 0.698 | 14:00 | 0.698 |

09:30 | 0.873 | 14:30 | 0.524 |

10:00 | 1.047 | 15:00 | 0.349 |

10:30 | 1.222 | 15:30 | 0.175 |

11:00 | 1.396 | 16:00 | 0.000 |

11:30 | 1.571 (= 90*π/180) |

False color composite (band 1–3) of a part of the study area from one of the ASTER scenes from 24 December 2007.

Footprints for the three stations and the scenes from 24 December 2007. Due to less unstable conditions, the flux footprints extend over a large area. As the color table is linear, only about 50% of the footprint is given in color.

Net radiation (option ‘best fit’) from one of the ASTER scenes from 24 December 2007.

Soil heat flux (‘Parlow/urban’) from one of the ASTER scenes from 24 December 2007.

Soil heat flux (‘Frey/NDVI’) from one of the ASTER scenes from 24 December 2007.

MAD of Q_{H} for the different methods of soil heat flux, parameters of the LUMPS scheme and atmospheric correction. MADs are given for simple pixel comparison and for the usage of the footprint model. Annotations are given in

MAD of Q_{LE} for the different methods of soil heat flux, parameters of the LUMPS scheme and atmospheric correction. MADs are given for simple pixel comparison and for the usage of the footprint model. Annotations are given in

Q_{H} modeled using the ‘Parlow/urban’ Q_{s} and the option ‘best fit’ from one of the ASTER scenes from 24 December 2007.

Q_{LE} modeled using the ‘Parlow/urban’ Q_{s} and the option ‘best fit’ from one of the ASTER scenes from 24 December 2007.

ARM heat fluxes. Q_{H} modeled using the ‘Parlow/urban’ Q_{s} and the option ‘best fit’ from one of the ASTER scenes from 24 December 2007.

ARM heat fluxes. Q_{LE} modeled using the ‘Parlow/urban’ Q_{s} and the option ‘best fit’ from one of the ASTER scenes from 24 December 2007.

Dates of ASTER acquisitions during the CAPAC campaign.

22nd November 2007 | 2(a + b) | X | X | X |

1st December 2007 | 2(a + b) | X | X | X |

24th December 2007 | 2(a + b) | X | X | X |

2nd January 2008 | X |

α and β parameter derived from the

^{th} Ramadan’ | ||||||
---|---|---|---|---|---|---|

Non-vegetated sector | 1.46 | 3.43 | 1.52 | 43.99 | 0.78 | 0.78 |

Vegetated sector | 1.64 | 7.2 | 3.17 | 33.16 | 0.71 | 9.70 |

Values from literature (Grimmond & Oke 2002) | 0.19 | −0.3 | 1.2 | 20 | 0.2 | 20 |

Mean absolute difference (MAD) of the four terms of the radiation balance. The values in brackets indicate the percentage of the MAD on the mean of the

Albedo [%] | 3.5 (14.8 %) | 2.3 (9.7 %) |

Irradiation [W·m^{−2}] |
43.0 (7.4 %) | 10.1 (1.7 %) |

Long wave emission [W·m^{−2}] |
8.4 (2.0 %) | Na |

Incoming long wave radiation [W·m^{−2}] |
20.4 (6.5 %) | Na |

Net radiation [W·m^{−2}] |
37.6 (11.6 %) | 22.3 (6.9 %) |

MAD of the ground heat flux, option ‘best fit’. The values in the third row indicate the percentage of the MAD on the mean of the

^{−2}] |
^{−2}] Single Stations | ||||
---|---|---|---|---|---|

‘Parlow/urban’ | 15.47 | 18.90 | 27.42 | 8.44 | 10.02 |

‘Frey/NDVI’ | 17.53 | 21.42 | 24.07 | 13.69 | 14.54 |

Annotations for

1 | ‘Parlow/urban’ | Campaign derived | best fit |

2 | ‘Parlow/urban’ | Grimmond [ |
best fit |

3 | ‘Frey/NDVI’ | Campaign derived | best fit |

4 | ‘Parlow/urban’ | Campaign derived | best guess |

5 | ‘Parlow/urban’ | Grimmond [ |
best guess |