In many regions of the world, water scarcity is an important issue for socio-economic development, and efficient management of water resources is required in order to ensure water and food security [1
]. Actual evapotranspiration (ETa), which corresponds to the sum of soil evaporation and vegetation transpiration, is a key land surface flux that significantly drives hydrological budget [2
], vegetation functioning and resulting agricultural production [3
], as well as boundary layer processes and regional climate [4
]. Further, ETa is strongly influenced by global change, including (1) climate forcing such as rainfall and evaporative demand and (2) anthropogenic forcing such as land use and agricultural systems [5
]. Therefore, accurate and consistent estimates of ETa at the extent of the small watershed are required to tackle the challenges related to water resource management. Besides, such observations over the long term are mandatory for (1) diagnosing the combined effects of the involved processes (i.e., climate and anthropogenic forcing, vegetation functioning, hydrological cycle), (2) prognosticating future trends by using modelling approaches based on calibration and simulation procedures [7
], and (3) validating remotely sensed products [8
To ensure accurate and continuous observations of ETa at the extent of the small watershed, the eddy covariance (EC) method is the reference technique for measuring the sensible (H) and latent (λE) heat fluxes, where λE corresponds to ETa. The EC method has been tested and proven at various spatial scales for a worldwide variety of land surface conditions, including crops, forests, snow, water bodies, urban areas, as well as mountainous and flat areas [9
]. EC method has several advantages such as high temporal resolution at hourly scale and spatial integration over large areas [10
]. However, EC measurements often experience large portions of missing data, as the consequence of sensor or power failures, maintenance and calibration procedures, improper weather conditions, and data rejection by quality checks [9
]. Gap filling methods are therefore necessary to obtain EC based continuous time series of land surface fluxes over seasonal or inter-annual periods. In order to provide accurate estimates of H and λE when data are missing, several gap-filling methods have been proposed. These methods rely on ancillary information in time or space: the mean diurnal variation method [11
], the regression method [12
], the evaluation of two-week average Priestley–Taylor coefficient [14
], the look-up table method [11
] and the multiple imputation [16
]. Most of gap filling methods were devoted to carbon dioxide measurements, for homogenous surfaces over flat or mountainous areas.
Hilly areas are widespread throughout the world. They experience intensification of rainfed agriculture, since topographical conditions permit the mobilization of water resources [17
]. They depict strong spatial heterogeneities, due to family farming that induces very small fields. For hilly and heterogeneous cropping systems, the land surface conditions that drive ETa (i.e., radiative regime, wind and turbulence regimes, water status) can be different from those occurring within homogenous surfaces over flat/mountainous areas.
The existing gap-filling methods have not been examined over hilly cropping systems at the extent of the small watershed. This is all the more critical that these specific conditions are likely to induce different relationships between ancillary information and flux measurements, as compared to those observed for homogeneous areas over flat or mountainous terrains. When dealing with hilly cropping systems, wind direction is an important parameter. First, the combined effects of hilly topography and wind direction induced changes in airflow streamlines and turbulent fluxes [21
]. At the field scale, Zitouna-Chebbi et al [22
] and Zitouna-Chebbi et al [23
] demonstrated the necessity to discriminate wind directions when processing EC data. Second, wind direction induces changes in the EC footprint that may subsequently spread over different patchworks of crop fields. Overall, changes in wind direction are likely to induce changes in the relationships on which rely gap-filling methods. This induces the necessity to evaluate the existing gap-filling methods, then to adapt these methods if necessary.
The current study aimed at evaluating a robust and widely used gap-filling method, for obtaining complete time series of ETa measurements over hilly cropping systems at the extent of the small watershed. We used a nearly four-years long EC measurements dataset, collected from a flux tower within an agricultural watershed. The latter was typified by hilly topography, and the footprint of the flux tower measurements integrated a patchwork of crop fields. The crops were rainfed, which minimized advection processes induced by changes in soil moisture. We evaluated the gap-filling method proposed by [24
], which is widely distributed through the REddyProc package version 0.6-0. We evaluated this method on λE for ETa, but also on H that is used to estimate water status indicators (e.g., Bowen ratio, evaporative fraction). Further, including H allowed to deepen our analysis of the gap-filling method. We compared the performance of the gap-filling method when used in its original version and when adapted to the conditions of hilly and heterogeneous cropping systems, i.e., by discriminating wind directions. The performances to be compared were related to both accuracy on flux estimates and gap-filling rates, at the hourly, daily and monthly timescales. Finally, daily and monthly values of ETa were documented and analyzed in terms of temporal dynamics.
The paper is structured as follows. Section 2
present the experimental strategy (site description, experimental design, data collection and processing, implementation and evaluation of the gap-filling method), the data set to be gap-filled, and the experimental conditions with a focus on meteorology. Section 3
reports the results obtained when (1) comparing of performances of the original and adapted versions of the gap-filling method; and (2) analyzing the temporal dynamics of the obtained Eta time series at the daily and monthly timescales. Conclusion discusses main outputs and future investigations.
3.1. Cross-Validation of REddyProc
The cross-validation of the REddyProc gap-filling procedure is presented in Table 2
. Over the considered period, 9 February to 15 September 2011 (10,464 30-min intervals), the number of 30-min intervals flux data remaining after quality control were 7255 (69%) and 4547 (43%) for H and λE, respectively. The number of artificial gaps introduced varied between 725 and 5078 (10% and 70% of the remaining data) for H, and between 454 and 3182 (10% and 70% of the remaining data) for λE. The artificial gaps introduced in this cross-validation analysis were adding to the already missing flux data (sixth and seventh columns of Table 1
), leading to larger percentages of actually missing flux data: between 38% and 79% for H and between 61% and 87% for λE.
The flux magnitudes were not affected by the random sampling of artificial gaps, since the average values ranged between 97 and 104 W·m−2 for H, and between 81 and 86 W·m−2 for λE. Regardless of artificial gap rate, the bias between the initial and the estimated fluxes was very low: between −3.4 and 5.6 W·m−2 for H, and between −1.9 and 1.5 W·m−2 for λE. The RMSE of the estimation increased slightly with the rate of artificial gaps: from 64 to 75 W·m−2 for H, and from 49 to 54 W·m−2 for λE. Accordingly, the corresponding R2 decreased slightly with the increasing rate of artificial gaps.
3.2. Application of REddyProc
3.2.1. Impact of Discriminating Wind Directions with REddyProc
presents the comparison of the sensible and latent heat fluxes estimated by REddyProc if splitting (RNS) or not (REP) the H and λE datasets according to wind direction. Figure 4
displays results at the hourly, daily and monthly timescales. We recall wind direction are labelled NW for north-western winds and S for southern winds.
At the hourly timescale and for NW winds, the sensible heat flux estimates HREP and HRNS were very similar, with a regression line close to the 1:1 line (slope = 1.07, intercept = 1.9), and a small dispersion (RMSE = 11.0 W·m−2). Conversely, under S winds, applying REddyProc without discriminating the wind directions (HREP) distinctly overestimated the sensible heat flux estimates (HRNS) obtained when discriminating wind directions (slope = 0.81, intercept = −1.9), with a slightly larger dispersion (RMSE = 15.7 W·m−2). Very similar results were obtained for the latent heat flux estimates: λEREP and λERNS were very close under NW winds (slope = 1.05, intercept = −0.5), with a small dispersion (RMSE = 12.2 W·m−2), whereas λEREP overestimated λERNS under S winds (slope = 0.81, intercept = 3.8), with a slightly larger dispersion (RMSE = 18.9 W·m−2).
For H and λE daily flux data obtained by integrating hourly values at the daily timescale (average of the 48 half-hourly fluxes, from 00:00 to 24:00), we obtained very similar results when considering REddyProc gap-filled time series with (RNS) or without (REP) discrimination of wind directions (see Figure 4
). Indeed, the regression lines between RNS and REP flux estimates were very close to the 1:1 line, and the corresponding RMSE values (4.5 and 4.6 W·m−2
for H and λE, respectively), were lower than those obtained at the hourly timescale.
Further, the daily flux data were integrated at the monthly time scale. As expected, we did not observe any difference, for both H and λE, when considering REddyProc gap-filled time series with or without discrimination of wind directions (REP vs. RNS). The dispersion around the regression line was low, 1.3 and 1.7 W·m−2 for H and λE, respectively.
3.2.2. Gap Filling Rates
The percentages of missing data remaining after application of REddyProc are given in the four last columns of Table 3
, for both ways of applying REddyProc (REP and RNS). REddyProc was able to fill gaps most of the time, except when periods with missing data lasted too long. We observed different results from one year to another, because of different periods with flux tower malfunctions.
In May and June 2010, the LI-7500 analyzer experienced a 34 days-long failure without λE measurements. REddyProc was able to fill all the missing λE data.
In December 2010 and January 2011, the flux tower experienced a 41 days-long failure without H and λE measurements. REddyProc was able to fill all the missing H and λE data.
From November 2011 to March 2012, the flux tower experienced several failures, without H and λE measurements for 99 and 126 days, respectively. Gap-filling for missing data was only partial, leading to a 99-day period without final data for both H and λE.
From October 2012 to May 2013, the flux tower experienced several failures, without H and λE measurements for 57 and 224 days, respectively. REddyProc was able to fill all the missing H data, but λE times series were not gap-filled during 221 days on 224.
Finally, the way of applying REddyProc, without (REP) or with (RNS) separating the wind directions, had no influence on the rate of gap-filled data (see Table 1
), except in 2013.
3.3. Seasonal Variations of Daily Surface Fluxes
The seasonal evolution of the sensible (H) and the latent (λE) heat fluxes, at the daily timescale, is presented on Figure 5
, along with the evolution of the evaporative fraction EF, evaluated as EF = λE/(H + λE). Both H and λE fluxes in Figure 5
were gap-filled by REddyProc without discriminating the wind directions (REP), since such discrimination had no impact at the daily timescale.
The daily values of sensible heat flux H exhibited a regular evolution over the seasons, with maximum values around 170 W·m−2 in summer (June to August), and minimum values in winter (November to February). Negative values of the sensible heat flux could be observed during winter, down to −50 W·m−2. The daily values of latent heat flux λE increased from winter to spring, reaching its maximum in April, around 120 W·m−2, which correspond to 3.5 mm·day−1. The latent heat flux decreased rapidly from the end of spring to summer, reaching very low values in August, down to 15 W·m−2 (0.5 mm·day−1). The latent heat flux increased in fall (around 80 W·m−2), and then decreased during winter (around 40 W·m−2).
The seasonal evolution of the evaporative fraction EF was rather regular, with low values, between 0.1 and 0.2, during summer, and with large values, between 0.8 and 1.2, during winter, the EF values exceeding unity corresponding to the periods during which the sensible heat flux was negative.
3.4. Monthly Evapotranspiration
Daily latent heat fluxes λE were monthly averaged, which permitted to reduce the day-to-day variability observed at the daily time scale, and next converted in actual evapotranspiration units (mm·day−1
). Figure 6
presents the seasonal evolution of actual evapotranspiration (ETa) and of its ratio to reference evapotranspiration ET0
, the latter being deduced from measurements at the meteorological station (see Section 2.5
). Actual evapotranspiration ETa followed a classical behaviour for Mediterranean rainfed crops, increasing from 1–1.5 mm·day−1
in winter to 2.5–3 mm·day−1
in April. From the end of spring to summer, ETa regularly decreased, reaching a minimum below 1 mm·day−1
in August. During fall, ETa increased again, as a consequence of rainfall events that are usual during that part of the year, then decreased in winter, as a consequence of the decrease of the reference evapotranspiration.
Inter-annual difference between monthly ETa was larger in spring and autumn, and it was lowest in summer. To remove the influence of inter-annual variability of climatic demand on that of ETa, we also addressed the ratio of ETa/ET0. As an example, the actual evapotranspiration was slightly larger in May 2012 than in May 2013, despite reference evapotranspiration rates were almost equal. Then, the inter-annual variability of the ETa/ET0 ratio was lower than that observed for ETa, and it was negligible in (i) April and June in 2011 and 2012, and (ii) November 2010 and 2011.
The results obtained when cross-validating REddyProc confirmed that the latter was able to provide un-biased and acceptable estimates of missing flux data, even for large rates of missing data (see Table 2
). The REddyProc appeared to be robust when facing large gap rates, as we observed a slight increase of relative RMSE values as gap rates largely increased. This was an important outcome, since adapting REddyProc to hilly cropping systems at the extent of the small watershed was likely to induce larger gap rates because of splitting the H and λE dataset according to wind direction. Finally, the RMSE values obtained were slightly better than those reported by [10
] who obtained values between 20% and 150% for an artificial gap rate of 20% with λE daytime conditions and different gap filling methods.
When comparing REddyProc retrievals with and without discrimination of wind directions, the obtaining of very different H and λE flux values for southern winds underlined the need to conduct such discrimination at the hourly timescale. This was ascribed to the prevalent replacement of missing flux data under southern (S) winds by flux data under north-western (NW) winds when applying REddyProc without discrimination of wind directions, since NW wind were more frequent that S winds in the original dataset (66% versus 33%, see Section 2.5
). Further, this is consistent with former studies that reported the need to discriminate wind directions when processing EC measurements in similar conditions [22
]. At the daily timescale, we observed very small differences between REddyProc retrievals with and without discrimination of wind directions. This was ascribed to three reasons. First, fluxes obtained at the daily timescale integrated both REddyProc gap-filled values and actual values, where the latter did not vary when applying REddyProc with or without discrimination of wind directions. Second, under NW wind directions that were dominant (66%), applying REddyProc with or without discrimination of wind directions led to very similar estimates of the fluxes at hourly time scale (see Figure 4
). Third, the difference between the two methods was proportional to the magnitude of the convective fluxes (see Figure 4
). Thus, integrating the fluxes at the daily timescale decreased the difference between the two methods, as large magnitude fluxes around noon were averaged with (1) low magnitude fluxes around early morning and late afternoon, and (2) night-time negative fluxes. Finally, we could not compare our results with former studies, because we did not find any literature report on this issue.
Applying REddyProc with or without discrimination of wind directions had no influence on the rate of gap-filled data, except in 2013 for which a failure of the wind wane at the meteorological station occurred concurrently to the failure of the flux tower. In this case, the concurrent failures prevented the application of the REddyProc with discrimination of wind directions, whereas it was possible to apply the REddyProc without discrimination of wind directions. Overall, REddyProc was able to find H and λE data with similar meteorological conditions, but difference in convective fluxes for similar meteorological conditions were likely to occur because of lack of a soil moisture proxy in the REddyProc method. Finally, the gap filling rate we obtained for H (between 65% and 100% of missing data) and λE (between 20% and 100%), could not be compared to outcomes from literature, owing to the lack of reports on this issue.
The sensible and the latent heat fluxes, as well as the evaporative fraction, exhibited large day-to-day variability, that could be ascribed to the variability of meteorological conditions, including rainfall events that might induce an increase of the latent heat flux during the next days. The seasonal dynamics we observed for the daily values of sensible of heat flux H were mainly driven by the temporal evolution of incoming solar radiation and air temperature. The maximum values we observed in April for latent heat flux λE were ascribed to the combined effects of vegetation growth, soil moisture availability, and intermediate values of reference evapotranspiration. The rapid decrease in latent heat flux E from the end of spring to summer was explained by vegetation maturation and next bare soil that combined with rainfall decrease. Finally, the latent heat flux increased in fall with the start of the rainy season, and then decreased during winter with the decrease of the reference evapotranspiration. In terms of flux magnitude, [36
] reported similar monthly values from scintillometer measurements within the same study area during spring (April–June) and summer (June–July) 2006, with values of 2.3 mm·day−1
and 0.5 mm·day−1
Inter-annual differences between monthly ETa were larger in spring and autumn, which was explained by the larger inter-annual variability in rainfalls for these periods of the year. In contrast, a lower inter-annual variability in ETa was observed in summer since rainfalls were negligible for this period. Subsequently to removing the influence of climatic demand, the inter-annual variability of the ratio ETa/ET0 was smaller than that observed for ETa. This ratio was very sensitive to the rainfall amounts during the fall, with an increase of ETa/ET0
arising sooner during the wet September months of 2010 and 2012 than during the dry September month of 2011. Finally, The ETa/ET0
values reported here were lower than 1.2, and therefore were within the confidence interval proposed by Allen [37
]. Also, the ETa/ET0
summer values (0.15 on average) were close to the Kc value proposed by FAO (The Food and Agriculture Organization) 56 [38
] for bare soils (i.e., Kcini for winter wheat).
The main outcomes of the current study are the following. First, the REddyProc method is robust when facing large rates of missing data to be filled. This is of importance when the dataset to be filled have to be split in accordance to different land surface conditions, wind direction in our case. This is also of importance since REddyProc relies on meteorological data that are usually collected along with EC measurement. Second, it appears to be necessary to discriminate wind directions when filling gaps within time series of land surface convective fluxes at the hourly timescale, in the context of hilly cropping systems at the extent of small watershed. This is consistent with former studies that reported the need to discriminate wind directions when processing EC measurements in similar conditions.
Future works should address the aforementioned issues by considering other gap-filling methods that rely on different ancillary information (i.e., rain or soil moisture that is a key driver of land surface evapotranspiration or evaporative fraction when latent heat flux λE data are missing and sensible heat flux H data are available). Also, our results gave great confidence in the observation of land surface fluxes by EC measurements over hilly cropping systems at the extent of small watershed. Then, the obtaining of complete time series for evapotranspiration at the extent of the small watershed opens the path for (1) cross-analysing these time series along with those of other components of the hydrological budget and (2) cross-analysing these times series along with trends in land use and climate forcing.