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Three operative models with minimum input data requirements for estimating the partition of available surface energy into sensible and latent heat flux using ASTER data have been evaluated in a semiarid area in SE Spain. The non-evaporative fraction (NEF) is proposed as an indicator of the surface water deficit. The best results were achieved with NEF estimated using the “Simplified relationship” for unstable conditions (NEF_{Seguin}) and with the S-SEBI (Simplified Surface Energy Balance Index) model corrected for atmospheric conditions (NEF_{S-SEBIt},) which both produced equivalent results. However, results with a third model, NEF_{Carlson}, that estimates the exchange coefficient for sensible heat transfer from NDVI, were unrealistic for sites with scarce vegetation cover. These results are very promising for an operative monitoring of the surface water deficit, as validation with field data shows reasonable errors, within those reported in the literature (RMSE were 0.18 and 0.11 for the NEF, and 29.12 Wm^{-2} and 25.97 Wm^{-2} for sensible heat flux, with the Seguin and S-SEBIt models, respectively).

The relationship between ecosystem latent heat (λE) and sensible heat (H) flux is critical to quantify the surface water deficit and to understand the hydrological cycle. The law of conservation of energy states that the available energy reaching a surface is dissipated as latent heat (λE) and/or sensible heat (H), the partition of which depends mostly on water availability. Factors affecting this relationship include longer-term interactions between biogeochemical cycles, disturbances and climate, and shorter-term interactions between plant physiology and the development of the atmospheric boundary layer [

Remote sensing is currently the only source of data providing frequent and spatially disaggregated estimates of radiometric temperature, albedo and surrogates of vegetation cover, variables that explain most of the partition of the available energy into H and λE. Therefore, model development using inputs from remote sensing data in the solar and thermal domain is a very active subject of research [

A widely used water deficit indicator is the evaporative fraction: EF=λE/(H+λE) [

We, therefore, propose using the non-evaporative (NEF) fraction to evaluate the surface water deficit, defined as:

In semiarid areas, the NEF should have a wider range of variability than the EF and a higher SNR (signal-to-noise ratio). It can be observed that the NEF is directly related to the Bowen ratio (β=H/λE). Introducing

The NEF is also similar to the Water Deficit Index (WDI) of [

The purpose of this study is to evaluate three simple operative models with minimum input data requirements for estimating the non-evaporative fraction (NEF) in southeast Spain. Two of the models are based on the “Simplified Relationship”, estimating daily H and Rn [

The study site, located in Almería (Spain) in the Mediterranean Basin, is characterized by escalating water demands for agriculture and tourism, leading to overexploitation of groundwater resources [

ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) data were used to calculate the non-evaporative fraction (NEF). ASTER is currently the only sensor collecting multispectral thermal infrared data at high spatial resolution, being very appropriate for model testing and direct ground comparison [

The study region (^{2} (36.95°N, 2.58°W). It is characterized by its heterogeneity, with altitudinal gradients ranging from sea level up to 2800 m (a.s.l.) in the Sierra Nevada Mountains. Precipitation and temperature regimes vary widely due to the orography [

In the center of the study site, the karstic landscape of the Sierra de Gádor mountain range, covering 552 km^{2}, consists of a series of thick carbonate rocks (limestones and dolomites), highly permeable and fractured with intercalated calcschists of low permeability underlain by impermeable metapelites [^{th} and 19^{th} centuries, when the original oaks (

Shrubland with a sparse cover of pine woodland (

The rest of the study site includes part of the Sierra Nevada Natural Park, composed of pine forest with oak relicts and shrublands. To the northeast, there is the Tabernas Lowlands, an area of badlands with complex topography. Along the ephemeral Andarax River, which flows past the capital city of Almeria, there is a mosaic of citrus orchards and vineyards. One of the most salient features of the scene is the large area of plastic greenhouses spreading over more than 330 km^{2}. This unique combination of land covers and uses makes this area an ideal pilot site for model testing. Two field research stations acquire data continuously in the study region,

Instrumental field data have been acquired continuously at the _{2}0 (both from Campbell Scientific Inc., USA). ^{2} flat area located at an altitude of 1600 m in the high, well-developed karstic plain of the Sierra de Gádor. Fetch is sufficient for the vegetation height and sensors. Vegetation cover is 50-60% and consists mainly of patchy perennial dwarf shrubs (30-35%) dominated by

Net radiation (NR-LITE; Kipp & Zonen, Delft, Netherlands), relative humidity (thermohygrometer HMP 35C, Campbell Scientific, Logan, UT, USA), soil temperature (SBIB sensors) and soil heat flux (HFT-3, REBS, Seattle, WA, USA) have also been continuously measured at the site since September 2003. Annual precipitation recorded during the last three hydrological years by a rain gauge mounted in 2003 varied considerably: 506.7 mm in 2003/04, 212.4 mm in 2004/05, and 328.1 mm in 2005/06.

The

Three perennial species dominate the landscape,

Experiments related to hydrology and erosion [

The eddy covariance system, currently located at

The variables used for this study include net radiation (NR-LITE; Kipp & Zonen, Delft, Netherlands), relative humidity (thermohygrometer HMP 35C, Campbell Scientific, Logan, UT, USA) sonic and soil temperature (SBIB sensors), wind speed, and soil heat flux.

ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) data on July 18, 2004, July 9, 2004 and June 19, 2005 at 11.00 UTC were acquired for this study. ASTER is an imaging instrument on-board of Terra, a satellite launched in December 1999 as part of the NASA's Earth Observing System (EOS). ASTER is a cooperative effort between NASA, Japan's Ministry of Economy, Trade and Industry (METI) and its Earth Remote Sensing Data Analysis Center (ERSDAC) [

The ASTER products used in our research included surface reflectance (2AST07) with a spatial resolution of 15 m (VNIR) and 30 m (SWIR), and kinetic temperature at 90 m (2AST0) with a surface temperature absolute precision of 1-4 K. No incidences have been reported for these scenes. The three images did not cover exactly the same area due to ASTER's off-nadir sensor pointing capability.

A digital elevation model (DEM) from the USGS (United States Geological Survey) with a 30 m resolution and a digital 0.5-m pixel orthophoto (from the Andalusian Regional Government) were used at different stages of the study.

Half-hourly air temperatures (°C) at the time of the satellite overpass (11.00 UTC) were acquired from meteorological stations for validation purposes. Ten or eleven stations were available for each image depending on scene coverage. Seven of the stations belong to the EEZA (Estación Experimental de Zonas Áridas), and the rest to the Andalusian Regional Government, (Red de Información Agroclimática de Andalucía).

Daily NEF (non-evaporative fraction) was estimated from ASTER and ancillary data using the ratio between daily sensible heat (H) and net radiation (Rn): H/Rnd.

Soil heat flux (G) can be considered negligible at a daily scale compared to the other components of the surface energy balance [^{-2}), H is the sensible heat flux (Wm^{-2}) and Rnd is the daily net radiation (Wm^{-2}).

Daily net radiation (Rnd) was calculated as the balance between incoming (↓) and outgoing fluxes (↑) of shortwave (Rs) and longwave (Rl) radiation. By agreement, incoming fluxes are positive and outgoing negative. Net radiation is the sum of net shortwave (Rns) and net longwave radiation (Rnl) [

First, Rni, instantaneous net radiation at the time of image acquisition, was calculated by estimating its four components:

The shortwave net radiation using remote sensing data was calculated as in

Rs↓ is the incoming solar radiation or incoming shortwave radiation, which was estimated at the time of the satellite overpass (11.00 UTC) using a solar radiation model [

Where ρ_{i} is reflectance at the surface for the band indicated by the subscript i. Reflectance was acquired from ASTER product 2AST07.

The longwave energy components are related to surface and atmospheric temperatures by the Stefan-Boltzmann Law. The outgoing longwave radiation was calculated at the time of image acquisition as in

Where σ is the Stefan-Boltzmann constant, (5.67×10^{-8} W m^{-2}), T_{s} is surface temperature (K), and ε_{s} is broadband emissivity for the surface, estimated based on the logarithmic relationship to NDVI as proposed by [

Radiometric surface temperature, T_{s}, was acquired directly from the ASTER kinetic temperature product retrieved by the TES (Temperature Emissivity Separation) algorithm.

An empirical function was used for the incoming longwave radiation Rl↓ [

_{air} is the air temperature and c and d are constants (0.261 and 7.77 10^{-4} K^{2}, respectively).

Daily net radiation (Rnd) (Wm^{-2}) was calculated from Rni by assuming Rnd/Rni≈0.3 ±0.03 at midday as proposed by [

The sensible heat flux (H) can be estimated by the turbulent transport from the surface to the lower atmosphere based on surface layer similarity of mean temperature and wind speed profiles using the resistance formula:
_{h} is a turbulent exchange coefficient dependent on wind speed, aerodynamic roughness length, roughness length for heat transfer and Monin-Obukov length [^{-1} (excess resistance) was added to the denominator of _{o}) and momentum (z_{oh}): Kb^{-1}=ln(z_{o}/z_{oh}). However, in practice, it is hard to get large-scale spatial estimates for all the variables in the resistance terms of H, therefore more operational parameterizations have been proposed.

One of the most widely used approaches to solving the surface energy balance that explicitly calculates H and Rnd is the so-called “Simplified Relationship” [_{d}) can be estimated from the difference between daily net radiation (Rnd) and daily sensible heat flux (H), by estimating H from the difference between instantaneous surface (Ts) and air temperatures (T_{air}) near midday, as in

The “Simplified Relationship” has been verified empirically and theoretically [

[^{-1}day^{-1} for stable atmospheric conditions (T_{s} - T_{a}<0) and 0.18 mmK^{-1}day^{-1} for unstable conditions (T_{s} - T_{air} > 0). At our study site at the time of image acquisition, unstable conditions tend to be prevalent [

Another operative approach for estimating H that also builds upon the simplified relationship was proposed by [_{s}-T_{air}) term. To estimate fractional cover NDVI was rescaled between values associated with sites where fractional cover is 0 (bare soil sites) and sites with vegetation cover =1, associated with dense forest sites. In our study site NDVI from associated to those two extremes was: 0.16 ± 0.012 (mean ± standard deviation) for bare soil sites and 0.68 ± 0.20 from complete vegetation cover. Mean values from bare soil and complete vegetation were taken to calculate B and n.

Hereinafter we will refer to NEF and H as calculated using the [_{Seguin} and H_{Seguin} and the one by [_{Carlson.} and H_{Carlson}.

Air temperature (T_{air}) is used to estimate sensible heat flux and net radiation. To avoid relying on meteorological information, T_{air} was estimated from the images using the NDVI-Ts triangle as proposed by [_{air}. T_{s} at the apex is found by locating minimum surface temperature areas in the scene. Those with the highest NDVI corresponding to forest patches are identified, and the average T_{s} for that selected region is calculated. Due to the altitudinal gradients in the study region, T_{air} must be corrected using the pixels at the region forming the apex as a reference altitude. Then positive corrections for altitude can be made for pixels below the baseline and vice-versa for pixels above it, considering a lapse rate of 6.5°C per 1000 m. This works better than considering a single T_{air} for the whole area, by assuming constant meteorological conditions at the blending height [

Another method of estimating the NEF, other than explicitly estimating surface energy balance variables, was derived from the S-SEBI (Simplified Surface Energy Balance Index) [_{s}) and albedo. It has been applied to estimate the evaporative fraction for crops and natural vegetation at different spatial scales [

Boundary conditions for the model can be extracted from the scatter plot of Ts and albedo. At low reflectance, Ts is almost constant with increasing albedo (Line “A” in _{max}). When albedo increases, Ts also increases because of reduced evapotranspiration at the expense of increased sensible heat flux. This is also within the “evaporation-controlled domain”. When albedo increases beyond a certain level, there is an inflection point, and Ts begins to decrease with albedo (line “B” in _{max}). However, the increase in albedo produces a decrease in shortwave net radiation reducing Ts. This is the “radiation controlled domain”. Rescaling each observed Ts according to these boundary conditions, “A” and “B” in _{obs} is the observed temperature, Ts_{λE} is the temperature at the lower boundary function or the evaporation-controlled domain and Ts_{H} is the temperature at the upper boundary function or radiation-controlled domain.

We modified the S-SEBI to account for variation in atmospheric conditions across the study site. Therefore, in this study, surface temperature (Ts) was standardized by T_{air} using the following equation to calculate NEF:
_{obs} is the observed difference between surface and air temperature, DT_{λE} is the difference between surface and air temperature at the lower boundary function or evaporation-controlled domain, and DT_{H} is the difference between surface and air temperature at the upper boundary function or radiation-controlled domain.

Both the upper and lower boundary functions were calculated by quantile regression [_{Seguin} and H_{S-SEBIt}.

The NEF and H calculated by this approach, in which the original S-SEBI (Simplified-Surface Energy Balance Index) formulation for calculating the EF (evaporative fraction) was modified by including T_{air}, are hereinafter referred to as NEF_{S-SEBIt} and H_{S-SEBIt}.

It is extremely complicated to validate surface energy fluxes estimated from remote sensing data due to limitated availability of measured surface fluxes for several surface types over large scales. In addition, field measurements and remote sensing footprints are not always comparable. In this paper we propose two validation procedures (a) Comparison of representative semi-arid vegetation surface types for which these field surface fluxes were available:

The eddy covariance system located at ^{2} since Fall 2003. At the ^{th} 2004 scene.

In addition, we used the wetland named “Cañada de las Norias” located in the greenhouse area as a validation site. For validation purposes we considered a field value for daily H=0, and therefore also for NEF=0, similarly to [

In shallow lakes such as “Cañada de las Norias”, heat accumulates during the day and supplies evaporative heat loss at night. Thus, although hourly changes in the storage term (G) can be high, on a daily basis (24 hr) G is smaller. For instance, in a similar wetland of the same area hourly G fits in summer a sinusoidal curve with midday peaks of around 50 Wm^{-2}[^{-2}[^{-2} with those extremes associated with rainy or cloudy days [

Regarding the sensible heat flux (H) on a daily basis its contribution to the wetland energy balance is minimum. In a semi-arid wetland daily H presented values ranging between ±20 Wm^{-2}. In a wetland nearby “Cañada de las Norias”, H contribution to heat budget was found to be less than 2% [

Because NEF_{Seguin} and NEF_{Carlson} models assume G=0, which is correct over land surfaces, modeled results over the lake were corrected just for validation considering NEF=H/(Rn-G) instead of NEF=H/Rn by assuming a daily G value in the wetland at the most between ±50 Wm^{-2} (around ±23% of Rn)-.

Estimated means of H, Rnd and NEF from each patch in the image and observed daily means from the eddy covariance or the SVAT model were compared in terms of R^{2}, RMSE (Root Mean Square Error), MAE (Mean Absolute Error), p, slope and intercept of the linear regression.

Spatial patterns with the NEF_{S-SEBIt} and NEF_{Seguin} were observed to be more similar to each other on the three dates than with the NEF_{Carlson} model, although NEF_{S-SEBIt} always yielded higher values. Across the study site, the lowest NEF with NEF_{S-SEBIt} and NEF_{Seguin} corresponded to water surfaces (sea and lakes), and high-altitude mountain forests. The highest NEF were located in the Tabernas lowlands which is plausible at this time of the year. However, NEF_{Carlson} values in the Tabernas lowlands where vegetation cover is scarce, are unrealistically low.

Linear regression of NEF on the three dates using all the pixels in each scene, including sea water, and the greenhouse area, shows (_{Seguin} and NEF_{S-SEBIt.} but not between NEF_{Carlson} and the other two models.

When model performance is examined more in detail for certain surface types on each date as a first approach to validating our results (_{Seguin} and NEF_{S-SEBIt} with a high NEF for dry, bare soil sites and low NEF in mountain forest sites. The NEF_{Carlson} seems reasonable for forest types, with values similar to NEF_{Seguin.} However, over bare soil surfaces, NEF_{Carlson} greatly underestimates NEF yielding even lower levels than forests (e.g., the limestone quarry would be evapotranspiring at the same rate as water according to NEF_{Carlson}). The [

It is important to mention that NEF_{S-SEBIt} and NEF_{Seguin} are very similar, but an offset equivalent to the NEF for water (lake at the middle of the greenhouse area) is observed for NEF_{S-SEBIt} suggesting a low wet edge, which would be easy to recalibrate. The fact that R^{2} >0.96 and the slope between NEF_{S-SEBIt} and NEF_{Seguin} is close to 1 on the three dates is very important, as these two models are calculated with very different approaches and NEF_{S-SEBIt} requires fewer input variables than NEF_{Seguin}.

Air temperature was required to estimate longwave incoming radiation, sensible heat flux and the S-SEBI_{t} evaporative fraction (

The overall adjustment is good (< 2°C), but T_{air} estimates are subject to local errors. Altitude is not the only factor affecting T_{air}, but using this approach has the advantage of not having to use meteorological station data. Also, any systematic error in T_{s} retrieval will propagate in T_{air}. These errors should therefore be compensated when calculating T_{s}-T_{air} differences for estimating sensible heat flux. In our case, this approach yields better results than the [

Results from estimating the Rnd using ASTER data show very good agreement with field data (^{-2}[^{-2}[

Emissivity values estimated in this work are reasonable according to reported values for soil and vegetation [

In the whole study region, maximum emissivity correspond to sites with complete cover such as forests, golf course, and irrigated orchards (0.97-0.98 depending on date). Estimated emissivity decreases with vegetation cover reaching values of 0.92-0.94 at the shrublands in Sierra de Gádor. The lowest emissivity values correspond to almond orchards dominated by bare soil signature (0.94-0.92), limestone quarry and mining areas (0.90-0.92).

The non-evaporative fraction (NEF) and the sensible heat flux H were validated using Eddy Covariance data at the

Validation results are similar for NEF and H (Wm^{-2}) (_{Seguin} and therefore, NEF_{Seguin}, provide the best overall performance being closer to the 1:1 line. Although the R^{2} is higher for H_{Carlson} and therefore, so is NEF_{Carlson}, their RMSE is still the highest of the three models.

At the _{Seguin} and H_{Carlson} around 30%. In addition to the simplicity of the modeling approaches, there is an error propagation from input data. Thus, although reported errors in T_{s} are within acceptable quality levels (< 4 K) they contribute to final error combined with the error in T_{air} estimates (< 2 K) and in the aerodynamic resistance that, in this case, is probably too high.

We should also be aware that the Eddy Covariance and Bowen Ratio techniques are subject to error. Uncertainty levels in the Eddy Covariance are around 20% [

Daily H estimates from remote sensing models usually contribute the highest uncertainty to the surface energy balance, with errors at a daily scale of around 20-30% or 1 mm day^{-1}, equivalent to ~29 Wm^{-2}[_{Seguin} and H_{S-SEBIt}, are below that threshold, but not for H_{Carlson}, Individual errors range between 3% and 30% for the worst cases (_{Carlson}) being the lowest in general for H_{S-SEBIt}.

In general, reported range of errors in H varies widely depending on surface type, image data, time average period, and model used. [^{-2} as acceptable for instantaneous H and 23 Wm^{-2} for daily H. In the literature, best case errors for instantaneous (half-hourly) and daily fluxes are around 10-22 Wm^{-2}[^{-2} for instantaneous H, while [^{-2} for instantaneous H using dual angle observations over a semiarid grassland in Mexico.

Our results for the NEF (non-evaporative fraction) are within errors reported for evaporative fraction at a daily scale from the SEBAL model, with a more complex parameterization, with RMSEs in the daily evaporative fraction (EF=1-NEF) between 0.10-0.20 [

Results from field validation confirm previous results about model performance for selected surface types as shown in

Three operative models for estimating the non-evaporative fraction (NEF) as an indicator of the surface water deficit, were evaluated in a semiarid area of southeast Spain. Of the three models evaluated, the NEF computed with the Simplified Relationship for unstable conditions [^{2}>0.97, p<0.0001). This is important, as the two algorithms are very different. One explicitly solves the variables in the surface energy balance, while the other uses a contextual relationship between albedo and surface temperature requiring fewer input variables. On the other hand, the spatial patterns obtained with Carlson's model [

Comparison to field data showed that net radiation (Rn) modeled with ASTER data produces very good results (R^{2}=0.91, p<0.0001), with an overall error within reported instrumental accuracy (< 5%). Validation of sensible heat flux (H) and NEF showed the most coherent spatial patterns with Seguin's approach [_{t} model. Of the three models, Carlson's approach had the highest RMSE. In semiarid sites with low NDVI, estimating the B exchange coefficient for sensible heat transfer based solely on NDVI produces unrealistic patterns, making it preferable to use a constant value of B, at least as a first approximation.

The errors found for NEF_{Seguin} and NEF_{S-SEBIt} are within those reported in the literature (RMSE for NEF are ~ 0.18 and 0.13 and for H are 29.12 Wm^{-2} and 25.97 Wm^{-2} for Seguin's and S-SEBI_{t} respectively). Given the simplicity of the models used, these results are very promising for operative monitoring of the surface water deficit and the partition of surface energy into sensible and latent heat flux.

This study received financial support from several different research projects: the integrated EU project, DeSurvey (A Surveillance System for Assessing and Monitoring of Desertification) (ref.: FP6-00.950, Contract n°. 003950), the PROBASE (ref.: CGL2006-11619/HID) and CANOA (ref.: CGL2004-04919-C02-01/HID) projects funded by the Spanish Ministry of Education and Science; and the BACAEMA (‘Balance de carbono y de agua en ecosistemas de matorral mediterráneo en Andalucía: Efecto del cambio climático’, RNM-332) and CAMBIO (‘Efectos del cambio global sobre la biodiversidad y el funcionamiento ecosistémico mediante la identificación de áreas sensibles y de referencia en el SE ibérico’, RNM 1280) projects funded by the Junta de Andalucía (Andalusian Regional Government). The authors wish to thank Ana M. Were and Angeles Ruiz for their helpful comments, S.Vidal and R.Ordiales for IT assistance, and Deborah Fuldauer for correcting and improving the English of the text. We thank two anonymous reviewers for improving this manuscript.

Study site in southeast Spain (Almería). The large image shows a 3D surface with elevation, and ASTER RGB false-color composite (15 m) taken on July 18, 2004. Three mountain ranges are visible: part of the Sierra Nevada, part of the Sierra Alhamilla and the Sierra de Gádor. White arrows show the location of the two research sites:

Scheme of the S-SEBI model (adapted from [_{obs} is the observed temperature, Ts_{λE} is the temperature in the evaporation-controlled domain and Ts_{H} is the temperature in the radiation-controlled domain.

NEF (non-evaporative fraction) using NEF_{Seguin}, NEF_{Carlson}, and NEFS-_{SEBIt.} models for July 18, 2004. NDVI levels on this date are shown in the grey scale image. The Sierra de Gádor in the center of the study site is outlined in black.

NEF (non-evaporative fraction) over selected surface types calculated by the NEF_{Seguin}, NEF_{Carlson} and NEF_{S-SEBIt} models. The first set of surfaces corresponds to undisturbed sites. Sierra N and Sierra S are pine forests on the northern and southern slopes of the Sierra Nevada Mountains, three densities of oak relicts correspond to: oaks (dense), oaks (sparse) and oaks. Pines correspond old reforested sites. The second set is for disturbed sites: greenhouses (Greenh), a strong burn scar (burnt), a limestone quarry (quarry), almond orchards (almond), and an abandoned mine (mine). The third set comprises miscellaneous sites: the Tabernas badlands, a lake, a golf coarse (golf), irrigated citrus orchards along the Andarax River (orchards); Ll. Juanes is the

Comparison of NEF (non-evaporative fraction) obtained with NEF_{Seguin}, NEF_{Carlson} and NEF_{S-SEBIt} models on the three dates using all the pixels in each image. RMSE is the root mean square error and p is the probability level associated with the regression.

_{Seguin}_{S-SEBIt} | ||||

R^{2} |
0.97 | 0.98 | 0.96 | |

p | 0.0000 | 0.0000 | 0.0000 | |

RMSE | 0.34 | 0.13 | 0.18 | |

slope | 1.0 | 0.83 | 0.94 | |

intercept | 0.34 | 0.18 | 0.20 | |

_{Seguin}vs. NEF_{Carlson} | ||||

R^{2} |
0.51 | 0.47 | 0.50 | |

p | 0.0000 | 0.0000 | 0.0000 | |

RMSE | 0.34 | 0.73 | 0.21 | |

slope | 0.49 | 0.66 | 0.84 | |

intercept | 0.08 | 0.05 | 0.16 | |

_{Carlson}vs. NEFS_{SEBIt} | ||||

R^{2} |
0.43 | 0.46 | 0.51 | |

p | 0.0000 | 0.0000 | 0.0000 | |

RMSE | 0.45 | 0.67 | 0.22 | |

slope | 0.24 | 0.34 | 0.58 | |

intercept | -0-006 | 0.59 | 0.35 |

Air temperature estimates at the study site. Mean Absolute Error (MAE) is the average absolute difference in residuals between estimated and measured air temperature at the meteorological stations. MAE after adjustment is the temperature corrected for a lapse rate of 6.5°C per 1000 m.

Reference altitude is the altitude of the pixels the apex temperature was taken from.

R^{2} (observed-predicted) |
0.61 | 0.74 | 0.67 |

MAE before adjustment (°C) | 4.31 | 3.40 | 2.68 |

MAE after adjustment (°C) | 1.96 | 2.07 | 1.93 |

T apex (°C) | 24.0 | 24.61 | 23.39 |

Reference altitude (m) | 1800 | 1833 | 1099 |

Daily Net Radiation Rnd (Wm^{-2}) of _{field}-Rnd _{Aster}). The % Error is calculated as (Rnd _{field}-Rnd _{Aster})100/ Rnd _{field.} For an overall error evaluation, the MAE (mean absolute error), the average AE, the mean % error, (% Error), R^{2} (Pearson correlation coefficient), p (probability), slope and regression intercept between field and ASTER results were calculated.

^{-2}) |
^{-2}) |
^{-2}) |
||||
---|---|---|---|---|---|---|

09-07-04 | Shrubs | Llano Juanes | 188.70 | 184.21 | 4.49 | 1.30 |

18-07-04 | Shrubs | Llano Juanes | 179.71 | 189.70 | 9.99 | 5.30 |

19-06-05 | Shrubs | Llano Juanes | 183.40 | 192.40 | 9.00 | 4.90 |

18-07-04 | Retama | Rambla Honda | 166.53 | 152.53 | 14.00 | -8.41 |

18-07-04 | Rambla Honda | 165.07 | 156.59 | 8.48 | -5.14 | |

18-07-04 | Rambla Honda | 159.28 | 155.97 | 3.31 | -2.08 | |

18-07-04 | Bare soil | Rambla Honda | 112.68 | 110.19 | 2.49 | -2.21 |

| ||||||

MAE | 7.39 | |||||

RMSE | 8.94 | |||||

Mean % error | 4.38 | |||||

R^{2} |
0.91 | |||||

p | 0.0008 | |||||

slope | 1.09 | |||||

intercept | -16.14 |

Field validation of the daily sensible heat flux (H) in Wm^{-2} estimated by the H_{Seguin}, H_{Carlson} and H_{S-SEBIt} models. AE is the absolute error (absolute difference between model and field observations). For overall error evaluation, the MAE (mean absolute error), which is the average AE, the R^{2} (Pearson correlation coefficient), p (probability), slope and intercept of the regression between field and ASTER were calculated.

^{-2}) |
^{-2}) |
^{-2}) |
^{-2}) |
^{-2}) |
^{-2}) |
^{-2}) | |||
---|---|---|---|---|---|---|---|---|---|

09-07-04 | Shrubs | Llano Juanes | 158.77 | 110.29 | 48.48 | 107.69 | 51.07 | 169.48 | 10.71 |

18-09-04 | Shrubs | Llano Juanes | 154.94 | 106.70 | 48.24 | 107.58 | 47.36 | 130.40 | 24.54 |

19-06-05 | Shrubs | Llano Juanes | 157.43 | 115.99 | 41.44 | 114.42 | 43.01 | 150.19 | 7.24 |

18-09-04 | Rambla Honda | 157.34 | 152.39 | 4.95 | 109.56 | 47.78 | 143.78 | 13.55 | |

18-09-04 | Rambla Honda | 133.15 | 139.38 | 6.24 | 80.56 | 52.59 | 139.06 | 5.91 | |

18-09-04 | Rambla Honda | 122.54 | 126.16 | 3.62 | 106.29 | 16.24 | 124.75 | 2.21 | |

09-07-04 | lake | Greenhouses | 0.00 | -27.33 | 27.33 | -0.93 | 0.93 | 46.61 | 46.61 |

18-09-04 | lake | Greenhouses | 0.00 | -19.07 | 19.07 | -1.34 | 1.34 | 21.54 | 21.54 |

19-06-05 | lake | Greenhouses | 0.00 | 7.06 | 7.06 | 5.01 | 5.01 | 49.41 | 49.41 |

| |||||||||

MAE | 22.94 | 29.48 | 20.19 | ||||||

RMSE | 29.12 | 36.58 | 25.97 | ||||||

R^{2} |
0.900 | 0.97 | 0.948 | ||||||

p | 0.00009 | 0.000001 | 0.00001 | ||||||

slope | 0.904 | 0.694 | 0.702 | ||||||

intercept | -9.833 | 1.66 | 39.304 |

Field validation of the NEF (non-evaporative fraction), NEF=H/(H+lE) NEF_{Seguin}, NEF_{Carlson} and NEF_{S-SEBIt} models. AE is the absolute error (absolute difference between model and field observations). When using the lake for validation, two cases have been considered G_{lake}=50 Wm^{-2} and G_{lake}=-50 Wm^{-2}. For an overall error evaluation, the MAE (mean absolute error), which is the average AE, the R^{2} (Pearson correlation coefficient), p (probability), slope and regression intercept between field and ASTER data were calculated (n=9 observations). For NEF_{Seguin} and NEF_{Carlson} overall error estimation has been performed twice, one with the dataset including the lake when G_{lake}=-50 Wm^{-2} and another with the dataset including the lake when G_{lake}= -50 Wm^{-2}, the latter in parenthesis the table.

09-07-04 | Shrubs | Llano Juanes | 0.88 | 0.61 | 0.27 | 0.59 | 0.29 | 0.93 | 0.05 |

18-07-04 | Shrubs | Llano Juanes | 0.92 | 0.59 | 0.33 | 0.61 | 0.31 | 0.72 | 0.2 |

19-06-05 | Shrubs | Llano Juanes | 0.88 | 0.62 | 0.26 | 0.61 | 0.27 | 0.79 | 0.09 |

18-07-04 | Rambla Honda | 0.97 | 1.00 | 0.03 | 0.72 | 0.25 | 0.94 | 0.03 | |

18-07-04 | Rambla Honda | 0.83 | 0.89 | 0.06 | 0.51 | 0.32 | 0.89 | 0.06 | |

18-07-04 | Rambla Honda | 0.79 | 0.81 | 0.02 | 0.68 | 0.11 | 0.8 | 0.01 | |

09-07-04 | Lake _{(G=50)} |
Greenhouses | 0.00 | -0.17 | 0.17 | -0.01 | 0.01 | 0.24 | 0.24 |

09-07-04 | Lake _{(G=-50)} |
Greenhouses | -0.11 | 0.11 | 0.00 | 0.00 | |||

18-07-04 | Lake _{(G=50)} |
Greenhouses | 0.00 | -0.12 | 0.12 | -0.01 | 0.01 | 0.10 | 0.10 |

18-07-04 | Lake _{(G=-50)} |
Greenhouses | -0.07 | 0.07 | -0.01 | 0.01 | |||

19-06-05 | Lake _{(G=50)} |
Greenhouses | 0.04 | 0.04 | 0.03 | 0.03 | |||

19-06-05 | Lake _{(G=-50)} |
Greenhouses | 0.00 | 0.02 | 0.02 | 0.02 | 0.02 | 0.21 | 0.21 |

| |||||||||

MAE Glake=50 (-50) | 0.14 (0.13) | 0.18 (0.17) | 0.11 | ||||||

RMSE Glake=50 (-50) | 0.18 (0.17) | 0.22 (0.22) | 0.13 | ||||||

R^{2} Glake=50 (-50) |
0.88 (0.89) | 0.97 (0.97) | 0.94 | ||||||

0.0002 | 0.000002 | 0.00001 | |||||||

p Glake=50 (-50) | (0.0002) | (0.000000) | |||||||

Slope Glake=50 (-50) | 0.94 (0.91) | 0.70 (0.70) | 0.75 | ||||||

Intercept Glake=50 (-50) | -0.08 (-0.05) | 0.01 (0.00) | 0.18 |