# Flux Measurements in Cairo. Part 2: On the Determination of the Spatial Radiation and Energy Balance Using ASTER Satellite Data

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{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 [4,14]. It inherently shows a high variability over heterogeneous surfaces. Several approaches using morphometric methods have been presented to account for this problem [15,16]. Also, the estimation of net radiation can be tricky, due to shading effects and multiple scattering of radiation by surface roughness elements. Nonetheless, several studies have used this method to derive urban sensible heat fluxes or the whole energy budget. In some cases, fairly good results were achieved, however other studies reported larger uncertainties and errors in the results [9,17,18]. In this paper, a bulk transfer approach is used, similar to the one described in [18], henceforward referred to as Aerodynamic Resistance Method (ARM).

## 2. Study Area

## 3. Data

#### 3.1. Satellite Data

#### 3.2. In situ Data

^{th}Ramadan’) were covered by all scenes. The following dates of ASTER data were available during the campaign in Cairo. An X in Table 1 indicates that the station is covered by at least one scene during this day. Scenes (a) are usually depicting the northern part of the agglomeration; scenes (b) show the southern part.

## 4. Methods: Radiation Balance

#### 4.1. Modeling of Net Radiation

^{*}[W·m

^{−2}] is given as

^{−2}], L↓ incoming long wave radiation [W·m

^{−2}], and L↑ outgoing long wave emission [W·m

^{−2}]. In the following, all terms will be explained separately.

#### 4.1.1. Broadband Albedo α

#### 4.1.2. 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 [32] was used. Using assumed synthetic emissivities, surface temperatures were then calculated for band 14. The assumed emissivities were 0.98 (water and pure vegetation) and 0.90 (urban and desert). In urban and agricultural areas of the ASTER scenes, where mixed pixels often occur, the formulas of [33] were used, incorporating the above-mentioned emissivities for pure pixels. The emissivities of the other bands were obtained by comparing their surface temperatures with the surface temperatures of the emissivity-corrected band 14. The resulting band emissivities (ε

_{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.

#### 4.1.3. Incoming Broadband Irradiation K_{↓} and Incoming Long Wave Radiation L_{↓}

_{↓}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 in situ measured K

_{↓}values from the CAPAC campaign [13] were used to iteratively find the optimal AOD values for the three available stations by minimizing the differences between the measured and the modeled K

_{↓}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 [34].

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

## 5. Methods: Heat Fluxes

#### 5.1. Modeling of the Ground Heat Flux Q_{s}

_{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 [3,5,7,35–37]. In this work the approach found in [38] and a new approach are presented. According to [38] the ground heat flux in urban areas is

_{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 Figure 8 in [13]). The reason for this offset is probably found in the measurement technique of in situ Q

_{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.

_{s}. However, none of these variables was able to improve the regression coefficients.

#### 5.2. LUMPS

_{H}, Q

_{LE}) and the available energy (Q* − Q

_{s}), β stands for the uncorrelated part [21]. In this study, both parameters were derived empirically from the in situ data of the CAPAC campaign. The values are derived for each station for a vegetated and a non-vegetated wind sector. Further, a comparison with a set of selected values from literature from [19] is given. Thereby the values from Mexico City are taken for the urban station. Table 2 gives the α and β values. The values were applied to the ASTER images according to the land uses: ‘urban’, ‘vegetation’ and ‘desert’. The LUMPS equations for the turbulent heat fluxes are as follows:

#### 5.3. ARM (Aerodynamic Resistance Method)

_{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}] [14]. Q

_{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 appendix.

_{h}can be determined with an approach using the roughness length, stability correction functions for momentum and heat, and the friction velocity [9]. The estimation of these parameters needs a detailed surface scheme, including a digital surface model of the urban area. However, no such detailed model was available for Cairo in sufficient accuracy; therefore, another empirical approach using radar data was pursued. Several studies have shown that aerodynamic roughness length can be represented by radar data [39–41]. Using the measurement data from the CAPAC campaign, an empirical relation was found between r

_{h}and the radar backscattering coefficient σ

^{0}of the ASAR image from 2 January 2008.

^{−1}]. The resulting equation is

#### 5.4. Source Footprint Models

## 6. Results

#### 6.1. Radiation Fluxes

^{−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.

^{−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.

#### 6.2. Ground Heat Flux

_{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. Table 4 shows the MADs of Q

_{s}.

_{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. Figures 4 and 5 show a sample from the scene (b) on 24 December 2007. The values of the River Nile are probably not realistic, as no special algorithm for water was used.

#### 6.3. LUMPS

_{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 in situ and one remote sensing value) of each turbulent heat flux were available for comparison; the agricultural station had only one pair, and the desert station also had three pairs. For simplicity, the agricultural pair is also addressed as MAD in the further analysis. The comparison was firstly conducted simply matching the value of the pixel of the mast’s location to the corresponding in situ value. In a second step, the footprint model was used for the retrieval of the remote sensing values.

_{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 [19]. The deviation of the agricultural station is extreme, even though the best fitting value for α proposed by [19] (α =1.2) was taken.

_{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 Figures 6 and 7).

_{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 [19] and using the ‘best guess’ option.

_{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.

_{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. Figures 6 and 7 show the MAD of Q

_{H}and Q

_{LE}for all calculated combinations.

_{LE}which were lower than the desert Q

_{LE}. Figure 9 shows Q

_{LE}modeled using the ‘Parlow/urban’ Q

_{s}and the newly-retrieved parameters for the LUMPS parameters.

_{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 Figure 8, the agricultural areas show clearly the lowest values, but the urban and the desert areas are almost similar. As mentioned before, Q

_{LE}was modeled quite well. This is attributed to the fact that the LUMPS parameters α and β deducted from the in situ measured values were retrieved for Equation (4), which estimates Q

_{LE}. Q

_{H}in Equation (5) then uses the same parameters. Due to the structure of the formula, it is not possible to retrieve α and β for Equation (5).

_{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).

#### 6.4. ARM

_{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.

_{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. Figures 10 and 11 show Q

_{H}and Q

_{LE}for the ‘best fit’ option and the ‘Parlow/urban’ Q

_{s}.

## 7. Discussion

- There is the error propagation from input variables, which was mentioned by [49]. Inaccuracies from input variables can result from various sources like BRDF effects, thermal anisotropy or an imprecise atmospheric correction. For example, in a single case at the desert station, the solar irradiation was underestimated about 99.6 W·m
^{−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 in situ ground heat flux are in the range of values found in [38]. It can be noted that differences are higher at the urban station compared to the agricultural and the desert station. This is probably due to the inability to measure directly the ground heat flux of an urban surface. So, the in situ data of the urban station are less accurate. The remote sensing ground heat flux was compared to 30-minute averages of in situ measurements. Direct comparison to one-minute averages would render extreme differences. This is because the storage heat flux as part of the ground heat flux showed extreme deviations due to short-time fluctuations of the surface temperature. Such high fluctuations can never be explained by instantaneous net radiation and vegetation indices only. - 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 situ measurements are scarce. This study has shown that adapting values from literature can lead to high mismatches.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 [6]. This problem, which applies only at the agricultural station, is not addressed by either the ARM or the LUMPS methods, and probably leads to higher differences at the agricultural station compared to the urban and the desert station.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 [51] or [29]. Having these magnitudes of closure gaps in mind, the results of the remote sensing fluxes do actually compare quite well.

## 7. Conclusions

^{−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.

_{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 in situ measured flux. At the agricultural station, the overall MAD was 40 W·m

^{−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%).

_{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.

_{H}of the urban station was 49 W·m

^{−2}, which is 26% of the mean in situ measured flux. At the agricultural station, the MAD was 1 W·m

^{−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.

## Acknowledgments

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## Appendix

- Desert:$$\epsilon =0.287+{\epsilon}_{\text{b}10}*(0.175)+{\epsilon}_{\text{b}11}*(-0.080)+{\epsilon}_{\text{b}12}*(0.068)+{\epsilon}_{\text{b}13}*(0.541)$$
- Vegetation:$$\epsilon =0.001+{\epsilon}_{\text{b}10}*(0.091)+{\epsilon}_{\text{b}11}*(-0.023)+{\epsilon}_{\text{b}12}*(0.349)+{\epsilon}_{\text{b}13}*(0.584)$$
- Water:$$\epsilon =-0.470+{\epsilon}_{\text{b}10}*(0.416)+{\epsilon}_{\text{b}11}*(-0.815)+{\epsilon}_{\text{b}12}*(-0.452)+{\epsilon}_{\text{b}13}*(0.163)+{\epsilon}_{\text{b}14}*(0.529)$$
- Urban:$$\epsilon =0.486+{\epsilon}_{\text{b}11}*(0.026)+{\epsilon}_{\text{b}12}*(0.091)+{\epsilon}_{\text{b}13}*(0.374)$$

_{spd}being the wind speed at the respective land use.

_{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

Hour | Γ | Hour | Γ |
---|---|---|---|

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) |

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

**Figure 2.**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.

**Figure 6.**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 Table 5.

**Figure 7.**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 Table 5.

**Figure 8.**Q

_{H}modeled using the ‘Parlow/urban’ Q

_{s}and the option ‘best fit’ from one of the ASTER scenes from 24 December 2007.

**Figure 9.**Q

_{LE}modeled using the ‘Parlow/urban’ Q

_{s}and the option ‘best fit’ from one of the ASTER scenes from 24 December 2007.

**Figure 10.**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.

**Figure 11.**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.

Date | Number of Scenes | Urban: ‘Cairo University’ | Agricultural: ‘Bahteem’ | Desert: ‘10th Ramadan’ |
---|---|---|---|---|

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 |

Urban: ‘Cairo University’ | Agricultural: ‘Bahteem’ | Desert: ‘10^{th} Ramadan’ | ||||
---|---|---|---|---|---|---|

α | β | α | β | α | β | |

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 |

**Table 3.**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 in situ measured values.

MAD ‘Best Guess’ | MAD ‘Best Fit’ | |
---|---|---|

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 %) |

**Table 4.**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 in situ measured values.

MAD [W·m^{−2}] | MAD [%] | MAD [W·m^{−2}] Single Stations | |||
---|---|---|---|---|---|

Urban | Agriculture | Desert | |||

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

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

## Share and Cite

**MDPI and ACS Style**

Frey, C.M.; Parlow, E.
Flux Measurements in Cairo. Part 2: On the Determination of the Spatial Radiation and Energy Balance Using ASTER Satellite Data. *Remote Sens.* **2012**, *4*, 2635-2660.
https://doi.org/10.3390/rs4092635

**AMA Style**

Frey CM, Parlow E.
Flux Measurements in Cairo. Part 2: On the Determination of the Spatial Radiation and Energy Balance Using ASTER Satellite Data. *Remote Sensing*. 2012; 4(9):2635-2660.
https://doi.org/10.3390/rs4092635

**Chicago/Turabian Style**

Frey, Corinne Myrtha, and Eberhard Parlow.
2012. "Flux Measurements in Cairo. Part 2: On the Determination of the Spatial Radiation and Energy Balance Using ASTER Satellite Data" *Remote Sensing* 4, no. 9: 2635-2660.
https://doi.org/10.3390/rs4092635