# Evaporative Fraction as an Indicator of Moisture Condition and Water Stress Status in Semi-Arid Rangeland Ecosystems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Materials

#### 3.1. Earth Observation Data

#### 3.2. Field Biomass and Flux Measurements

^{−1}) was measured every minute by the tower instruments at a height of 2.5 m; these data are supplied to the user from the CarboAfrica project through FLUXNET measurement network as the average over 30-min periods [60]. This variable is available as a Level 2 product, i.e., not gap-filled, but checked/filtered for out-of-range values or clearly wrong data [60]. The daily latent heat flux data (W∙m

^{−1}), processed with despiking, double rotation and gap filling following the indications of [61], were obtained from the publication of [62]. Both fluxes are available for the period between June 2005 and June 2007, including the wet season of 2005 and 2006.

## 4. Method

#### 4.1. Estimation of Evaporative Fraction

_{0}is the soil heat flux and H is the sensible heat flux.

_{n}− G

_{0}):

_{0}represents the albedo, while T is the land surface temperature.

_{H}and the temperature pixel T

_{S}by the difference between T

_{H}and T

_{λE}:

_{si}is the temperature value of the pixel i and T

_{Hi}and T

_{λEi}are respectively the maximum and minimum temperature value derived by the dry and wet edge functions for a given albedo value α

_{i}.

#### 4.2. Evaluation of the Estimated EF

_{d}and λE

_{d}are the daily net radiation and the daily latent heat flux, respectively.

#### 4.3. Biomass Estimation

^{JASO}).

^{8D}is the estimated water stress from Equation (6), s is the site and n is the cardinality of the 8-day EF data for each month.

^{m}) was calculated to represent the total dry biomass produced during every month at each site:

^{10D}is the 10-day biomass estimation product, t is the number of DMP data within the month and s is the site.

^{m}values were than integrated and annually cumulated by the following equation for each site:

^{m}and DMP

^{m}are the variable obtained from Equations (8) and (9), s is the site and 4 is the number of months in the JASO period.

^{JASO}*, the comparison between observed and estimated values were performed and difference-based statistics [68] together with regression analysis and Akaike information criterion (AIC) [69], Equation (11), were conducted.

## 5. Results and Discussion

#### 5.1. Dry and Wet Edge Statistics

#### 5.2. Evaluation of EF Spatial Patterns

#### 5.3. Comparison of Seasonal EF Estimations with Eddy Covariance Data

#### 5.3.1. Temporal Dynamics of the Variables

#### 5.3.2. Correlation Analysis with ET

^{2}= 0.62; 2006, r

^{2}= 0.45) were not significantly different (p < 0.05). This correlation is biased by estimated EF in the late, dry season (January–May), when no rain and no vegetation are present, confirming that EF is noisy in the dry season [39].

^{2}= 0.64), since it represents the climatic driving force of evaporative and transpirative processes. In order to investigate if EF can improve the capability to explain the variance of ET, a multiple regression was performed between ET as a dependent variable and two independent variables, the measured Rn and the simulated EF.

#### 5.3.3. Biomass Estimation Improvements Using EF Correction

^{JASO}) and biomass estimation corrected by EF (DMP

^{JASO}*) were compared with available annual production data over three test sites in Niger.

^{JASO}. The three sites show different correlations: in particular, Site 1 (black dots) presents little correlation (r

^{2}= 0.49, intercept = 1300, slope = 0.3); Site 2 (blue squares) shows an average correlation (r

^{2}= 0.51, intercept = 700, slope = 1.1); and Site 3 (red triangles) has a high correlation (r

^{2}= 0.66, intercept = 400, slope = 0.3). All three sites have the typical Sahelian biomass production [76], ranging from 100 (kg·ha

^{−1}), in adverse years, to 20-times higher production in favorable climatic conditions.

^{JASO}is able to detect the field biomass variability with site-specific, good correlation; however, the analysis of intercept and slope variability across sites indicates that the model is not able to give a robust quantitative biomass estimation. Indeed, the DMP algorithm does not take into account distinct efficiency factors in the conversion of light into biomass among different vegetation types. It should be reminded that, despite the three test sites featuring the same land cover and eco-region, the actual floristic composition and ecological characteristics could be much more different.

^{JASO}*) over the three sites. The plots show a general increase in the capacity of the remote sensing estimation in each site to detect the variability of the field measurements if water stress is taken into account, as indicated by the increasing of regression coefficients. Moreover, in particular, the EF has reduced the overestimation of the model for poorly productive years, as shown by intercepts closer to zero.

^{JASO}(gray dots) and DMP

^{JASO}* (black dots). The data close to zero are near the population average, while data values below or above zero indicate a positive or a negative anomaly, respectively. The top right and bottom left corners indicate that years were estimated, and the measured variables’ data are in agreement.

^{JASO}* (r

^{2}= 0.73, p < 0.001) indicates that there is a significative increase in the capacity of the remote sensing estimation to explain the variance of annual field biomass measurements if water stress (EF) is taken into account.

^{JASO}*) is confirmed by the improved model performance, indicated by the higher correlations shown in Figure 9c and the lower AIC value (106) compared with the one obtained with DMP

^{JASO}(112).

## 6. Conclusions

^{2}= 0.54, p < 0.001) acquired for two years (2005–2006) by an eddy flux tower in Niger. The total variance of evapotranspiration is mainly explained by the measured net radiation (64%, p < 0.001), while the estimated evaporative fraction significantly improves the model with a further 6% of variance explanation (p < 0.01). These results demonstrate that the satellite-derived evaporative fraction is a reliable indicator of moisture, useful for savannah status monitoring.

^{2}= 0.73, p < 0.001) compared to the performance of the basic satellite product (r

^{2}= 0.54, p < 0.001). The appropriate water efficiency term derived from optical and thermal remote sensing data represents an advancement over previous studies conducted using only the evaporative fraction derived by in situ eddy covariance data.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The study area overlaid on the regional GlobCover (GC) map of Africa [51]; the red star shows the position of the eddy covariance station; the red diamonds represent the field sites; the blue lines indicate the isohyet boundaries of 200–600 mm/year.

**Figure 2.**Scatterplot between surface albedo and LST. Blue circles correspond to minimum temperature values for each albedo class, which are used to compute the wet edge (lower limit of the graph) through linear regression. Red circles correspond to the maximum temperature values for each albedo class, which are used to compute the dry edge (upper limit) through linear regression. T

_{H}(maximum temperature) and T

_{λE}(minimum temperature) represent the values used in the calculation of the EF for the pixel i.

**Figure 3.**Flowchart for the evaporative fraction estimation from the MODIS products of albedo and land surface temperature.

**Figure 4.**Eight-day average values of the intercept (

**a**) and slope (

**b**) obtained from dry and wet edge lines for the 2000–2009 period. Shaded gray areas represent the dry season. Plots show three albedo-LST scatterplots for the year, 2009.

**Figure 5.**The map of the average EF (

**a**) and relative standard deviation (

**b**) derived from 448 EF eight-day maps (2000–2009). Isohyets were calculated from rainfall estimation (RFE) data for the same period. The hyper-arid areas (<200 mm∙year

^{−1}) are masked out, and the GlobCover map is in the background.

**Figure 6.**Percentage of GC classes over the study area (codes and map color are reported) and the statistics of EF data for each LC classes (average (AVG) and relative standard deviation (RSD)). Red and green indicate land cover with a lower of a higher EF average, respectively.

**Figure 7.**From top to bottom, the temporal behavior of daily net radiation; daily evapotranspiration; EF-derived from the eddy covariance tower data at the Wankama site (black lines) together with eight-day EF estimation from MODIS data (red dashes); decadal NDVI-VGT (green line); decadal precipitation (blue bars), eight-day MODIS albedo (gray line) and eight-day MODIS temperature (yellow line) for 2005 (

**a**) and 2006 (

**b**). Vertical lines represent the start and finish of the JASO period, doy the Day Of the Year.

**Figure 8.**Correlation between estimated EF (y-axis) and measured ET (x-axis) for both years 2005 (gray) and 2006 (purple) (n = 57).

**Figure 9.**The correlation between annual biomass samples and satellite estimation DMP

^{JASO}(DMP, dry matter productivity) (

**a**), DMP

^{JASO}* (

**b**) and normalized data (

**c**) (n = 19). Black dots for Site 1, blue squares for Site 2 and red triangles for Site 3. Black and gray diamonds represent normalized DMP

^{JASO}and DMP

^{JASO}, respectively. The dotted line indicates the 1:1 line.

Site | #Data | Period | AVG (kg/ha) | Max (kg/ha) | Min (kg/ha) | Stand Deviation (kg/ha) |
---|---|---|---|---|---|---|

Site 1 | 6 | 2003; 2005–2009 | 963 | 1,463 | 342 | 508 |

Site 2 | 8 | 2000; 2002–2009 | 371 | 1,047 | 0 | 378 |

Site 3 | 5 | 2001; 2005; 2007–2009 | 888 | 1712 | 326 | 614 |

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## Share and Cite

**MDPI and ACS Style**

Nutini, F.; Boschetti, M.; Candiani, G.; Bocchi, S.; Brivio, P.A.
Evaporative Fraction as an Indicator of Moisture Condition and Water Stress Status in Semi-Arid Rangeland Ecosystems. *Remote Sens.* **2014**, *6*, 6300-6323.
https://doi.org/10.3390/rs6076300

**AMA Style**

Nutini F, Boschetti M, Candiani G, Bocchi S, Brivio PA.
Evaporative Fraction as an Indicator of Moisture Condition and Water Stress Status in Semi-Arid Rangeland Ecosystems. *Remote Sensing*. 2014; 6(7):6300-6323.
https://doi.org/10.3390/rs6076300

**Chicago/Turabian Style**

Nutini, Francesco, Mirco Boschetti, Gabriele Candiani, Stefano Bocchi, and Pietro Alessandro Brivio.
2014. "Evaporative Fraction as an Indicator of Moisture Condition and Water Stress Status in Semi-Arid Rangeland Ecosystems" *Remote Sensing* 6, no. 7: 6300-6323.
https://doi.org/10.3390/rs6076300