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’.
6.1. Radiation Fluxes
The calculated radiation fluxes from the ‘best guess‘ and the ‘best fit‘ option were compared to the in situ measured fluxes (original 1 min averages) using the values of the pixel directly associated with the station. Assuming a purely cosine dependent sensor response of the in situ radiation measurement instrument, reflected radiation for the agricultural and the desert station comes from a circular area within a radius of 11 m. In the case of the urban station however, the radius is much larger. Though, using only the height difference between the sensor and the roof, about 90% of the flux would come from a circle within a radius of 45 m.
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 Table 3
. The critical term is the albedo, which has a MAD of 2.3% in the ‘best fit’ option. All differences of the albedo were of such magnitude, independent on the station. The high MAD of the ‘best guess’ irradiation of 43.0 W·m−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 in situ radiation values were measured using CNR1 from Kipp & Zonen. The specification sheet lists the expected accuracy for the daily totals to be ±10%. A calibration of the instruments at the end of the campaign improved the accuracy to about 5–10% for single measurements. Having this in mind, the achieved 11.6% accuracy for the net radiation using the ‘best guess’ option is good.
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 [34
]. For the ASTER scenes used, a maximum error of 2% is estimated for this geometry effect.
shows the ‘best fit’ net radiation from scene (b) of 24 December 2007 for a part of Greater Cairo. The three main landscape features can be easily recognized: the desert areas in the right part of the image with low net radiation values, the agricultural fields in the upper left part with high net radiation values and the urban parts with medium net radiation values. The River Nile is also clearly visible with very high values.
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.
QH and QLE estimated with the LUMPS scheme were calculated using both the ‘Parlow/urban’ and the ‘Frey/NDVI’ approaches for Qs. 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.
The parameters from [19
] produced fairly good QH
at the desert station. Taking the ‘Parlow/urban’ method for Qs
and using the ‘best fit’ option for Q*, the MAD of QH
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
and 41.3 W·m−2
and 116.6 W·m−2
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.
Of course, the LUMPS parameters derived from the measurement data performed better for both the urban and the agricultural station. MAD of QH
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 QLE
are 18.3 W·m−2
, 24.9 W·m−2
, and 15.1 W·m−2
(compare Figures 6
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’ Qs
were then 37.0 W·m−2
, 5.2 W·m−2
and 20.0 W·m−2
and 20.5 W·m−2
, 32.1 W·m−2
, and 14.8 W·m−2
. The MAD also increased in almost all cases, taking the parameters from [19
] and using the ‘best guess’ option.
MADs for QH and QLE change only at the agricultural station, when using the ‘Frey/NDVI’ approach for Qs. There, the MAD of QLE decreases to 16.2 W·m−2, and MAD of QH 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 QH
MAD values only improved significantly at the agricultural station, and in some cases, the LUMPS parameters from literature were used. QLE
sometimes improved, other times not. Overall, the effect of the footprint models was ambiguous. Figures 6
show the MAD of QH
for all calculated combinations.
Spatial analysis of the LUMPS heat fluxes showed that the different approaches produced fairly different patterns. Following [13
], it was assumed that the sensible heat flux should be highest in desert areas, closely followed by urban areas and lowest over agricultural fields. However, the latent heat flux should be highest over the agricultural fields, followed by the urban areas, and be lowest in the desert areas. This pattern was partly fulfilled by the LUMPS approaches. The latent heat flux was modeled fairly in accordance with this pattern in almost all cases. Only the approaches using the parameters of [19
] rendered urban QLE
which were lower than the desert QLE
. Figure 9
modeled using the ‘Parlow/urban’ Qs
and the newly-retrieved parameters for the LUMPS parameters.
however, did not always follow this order. On one day for example, 22 November 2007, mean agricultural QH
was higher than mean urban or mean desert QH
. In Figure 8
, the agricultural areas show clearly the lowest values, but the urban and the desert areas are almost similar. As mentioned before, QLE
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 QLE
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)
Looking at the Bowen ratio β (=QH/QLE), 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).
QLE estimated with the ARM method was calculated with the ‘Parlow/urban’ Qs only, as no significant influence was found from taking either the ‘Parlow/urban’ or the ‘Frey/NDVI’ QS in the analysis of the LUMPS results. Generally, MAD of QH and QLE 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 QH 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 QLE 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 QLE 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. QLE
was modeled correctly, with the agricultural QLE
the highest, the desert QLE
the lowest and the urban QLE
somewhere in between. Also, QH
showed a reasonable distribution. Figures 10
for the ‘best fit’ option and the ‘Parlow/urban’ Qs
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.