The study sites are located in Central-Southern Burkina Faso and northern Ghana. The area belongs to the northern zone of West Africa’s Sudanian savanna belt (White, 1983). The climate is semi-arid and highly influenced by the West African monsoon (Berger et al., 2019). There is a pronounced dry season between November and March, a rainy season between May and September, and two transitional periods in April and October. The mean annual precipitation ranges between 700 and 1,100 mm (Bliefernicht et al., 2018). The region is marked by steep local gradients in land use intensity (Berger et al., 2019). For analyzing the influence of land use change on water, energy, and CO₂ cycles, the three measurement stations were set up in areas with different land use practices that lead to different vegetation covers (Figure 1). In Nazinga there is near-natural pristine savanna due to wildlife conservation, in Kayoro there is a mixture of fallow and cropland, and Sumbrungu is a highly degraded grassland site, occasionally used as pasture for cattle and sheep (Quansah et al., 2015). Other site characteristics like climate, soil, and topography as well as the latitude were chosen to be as similar as possible to assure that long-term differences between the analyzed variables were primarily the result of land use changes. The instrumentation is nearly identical at each site but with individual measurement heights (Table 1), depending on the respective mean vegetation height (Bliefernicht et al., 2018). For a more detailed description of the three sites and the instrumentation of the EC stations, refer to Quansah et al. (2015) and Bliefernicht et al. (2018).

For the study we used EC data from 10/18/2012 to 09/26/2016 (Table 1) with the variables needed for the energy budget as well as turbulence data. The fluxes were integrated over half-hour periods from the covariance of vertical wind velocity and gas concentrations measured at 20 Hz frequency using 3-dimensional sonic anemometers (Gill WindMaster; Gill Instruments Ltd., Lymington, Hampshire, England) and open-path infrared gas analyzers (LI-7500A; LI-COR, Lincoln, NE, USA). All sites are equipped with the same instrumentation. The raw turbulence data and the three-dimensional wind speeds were processed with the “Turbulence Knight” (TK3.1) software. The software performs several kinds of post field processing and produces turbulence fluxes automatically (Quansah et al., 2015; Soltani et al., 2018). It uses standardized quality assessment routines and user-specified consistency limits to detect and reject physically or electronically impossible values of the measurement data including CO₂, sensible and latent heat fluxes (Quansah et al., 2015; Mauder and Foken, 2015). For more information about the calculation of the turbulent fluxes and quality control used by the TK3.1 software refer to Mauder et al. (2013) and Mauder and Foken (2015). It is important to note that this analysis is based exclusively on raw observational data, with no gap-filling algorithms applied.

Moreover, we performed a quality control of the aggregated 30-min measurements for each energy balance variable and conducted several subsequent calculations to determine the required variables for the EBC. At each EC station, the ground heat flux (G) was measured with three heat flux plates at the same depth, and we performed a cross-comparison of those time series by using correlation measures to eliminate unreliable time series. In Nazinga we only used the measurement information from two sensors for the calculation of the mean ground heat fluxes, as the central device showed much lower correlation with the other two devices here, possibly indicating a defect in the sensor. Because the exchanges of longwave radiation LWx [W/m²] between the instrument and the ground or atmosphere were recorded instead of the longwave radiation, which is needed, we applied the sensor body temperature T [K] to obtain this variable:

We applied a fuzzy rule-based classification of atmospheric circulation patterns (CPs) introduced by Bliefernicht et al. (2022) to acquire a better understanding of how the distinct phases of the West African monsoon (WAM) impact the EBC and to use this additional information for the development of the post-closure approaches. In general, this classification was developed to relate large-scale monsoon features such as the West African heat low (WAHL) (Lavaysse et al., 2009) to daily rainfall variability in Central Burkina Faso (Bliefernicht et al., 2022). Depending on the spatial patterns of mean sea level pressure anomalies (Figure 2) and the movement of the WAHL, the different WAM seasons can be divided into three main periods: CP1, CP6, CP7 are predominant during the dry period, CP2, CP3, CP8 during the transitional periods and CP4, CP5 dominate during the wet period. In this study, we transfer the classification method to the period of 2012–2016 using ERA5-reanalysis data (Hersbach et al., 2020) to derive a time series of daily CPs. Table 2 shows the wetness index (WI) of each CP and some further statistics. For a more detailed description of the methods and CPs, see Bliefernicht et al. (2022).

In this study, three different closure approaches to minimize the bias of the EC measurements are applied: the standard Bowen-ratio (BR) method after Mauder et al. (2013), a novel correction method that is based on quantile mapping of the empirical distributions from the EBC variables, hereafter referred to as QM method, and an extension of the QM method conditioned on regional CPs, hereafter referred to as QM-CP method.

The performance of EC measurements is usually assessed through a scatter plot between the available energy and turbulent fluxes (Mauder et al., 2010; Soltani et al., 2018; Eshonkulov et al., 2019; Grachev et al., 2020). In contrast to other post-processing studies (e.g., Eder et al., 2014; Imukova et al., 2016; Xin et al., 2018), we performed here a more detailed analysis to determine if the correction method could eliminate the bias of the EC measurements. Therefore, we implemented some additional bias measures to assess the quality of the approach quantitatively.

The half-hourly averaged data sets of Rn, G, LE and H for Nazinga, Kayoro and Sumbrungu were used to evaluate the performance of the EC measurements for the study period. We calculated the sums of Rn − G and H + LE for all joint measurement pairs over the whole time period and visualized them in a scatter plot. We performed a linear regression between the half-hourly averaged turbulent fluxes (H + LE) and the available energy (Rn − G):

where m is the slope and b the intercept. Under best conditions, m should be close to 1 and b close to zero, indicating a nearly perfect closure of the energy balance. However, the available energy is usually found to be 10–30% larger than the turbulent fluxes (Foken, 2008; Stoy et al., 2013; Mauder et al., 2020; Finnigan et al., 2003). We calculated several performance measures to evaluate the quality of the EBC for the whole investigation period, four different seasons (DJF, MAM, JJA, and SON) and eight different CPs at each site. First, we calculated the mean values of the sum of TF (x¯TF) and the sum of AE (x¯AE)

to determine the first-degree bias (B₁):

A negative bias indicates an average underestimation of the turbulent fluxes. Moreover, we calculated the standard deviation of the sum of TF (sTF) and of AE (sAE):

to determine the second-degree bias (B₂):

A negative value indicates an underestimation of the variability of the sum of TF. Additionally, a relative bias measures, RB₁, was calculated, as ratio from the B₁-value to the mean sum of the available energy.

Additionally, we implemented a conditional bias measure to evaluate the overall performance of each correction method. Therefore, for each site we calculated the occurrence frequency of each CP (f_k) over the study period. Then, the absolute value of the bias of each CP was weighted according to its f_k. These conditioned bias values for each CP we summed up, providing a conditional bias measure (CB) for each site and each correction method. We performed this for B₁ as well as for B₂ (CB₁ and CB₂, respectively):

with K as the number of CPs and f as the relative frequency of the CP within each measurement site.

Maintaining a flux site in quite remote regions can be challenging and different problems occurred during the measurement period at the three sites. Especially the natural site Nazinga is not reachable during the wet season. Thus, sensor defects that require maintenance can cause big data gaps. Further, the theft of solar panels, entire devices, and attacks on guards were also challenges that occurred (Bliefernicht et al., 2018). We only considered the datapoints when all four energy balance variables were available. Therefore, the data availability for calculating EBC is even lower. Nonetheless, the data from the three investigated sites allows insights into the hydrometeorological characteristics of the region (Figure 4). Similar patterns of net radiation can be seen at all three sites, whereby a seasonal cycle with higher net radiation can be observed during the northern hemisphere summer. The ground heat flux shows a similar seasonal pattern. However, it peaks during the dry season (northern hemisphere winter) where more sun can reach the ground due to a less cloudy sky. Consequently, the available energy Rn − G is slightly higher during the wet season in summer than during the dry season in winter. The latent heat flux also shows a clear seasonality with higher values during the wet season, where the soil water availability is higher, and more energy can be transported through evapotranspiration. In the drier winter months, the latent heat flux becomes very small, and more energy is transported through sensible heat. This pattern can be seen across all land use sites. However, at the natural site in Nazinga (Figure 4a) we also see high seasonal differences in the sensible heat flux with lower values in the wet season and higher values in the dry season. At the other two sites with less vegetation height and cover, Kayoro and Sumbrungu (Figures 4b,c, respectively), we observe less pronounced seasonal variations in the sensible heat flux. The latent heat flux further has lower values at these two sites. While Nazinga is characterized by tall grasses of up to 2.5 m, dominated by perennial C4 grasses and a dense savanna woodland (Berger et al., 2019), at Kayoro the grass layer is much lower (around 1 m). The tree layer is more sparse and influenced by grazing animals. In Sumbrungu the herbaceous layer is only about 10 cm high (Berger et al., 2019). Thus, the vegetation in Nazinga offers more plant mass and surface for transpiration of water, facilitating a higher latent heat flux. This shows how the relative composition of tree and grass canopy that have different capacities for photon interception and absorption as well as transpiration (Kelliher et al., 1993; Miranda et al., 1997) strongly influences the surface energy balance of a landscape. These eco-physiological processes are especially intricate in savanna ecosystems, as the two layers (tree and grass) introduce multiple levels of complexity, differing in their phenological cycle (Whitecross et al., 2017), rooting depths (Bachofen et al., 2024) and water use strategies (Miller et al., 2010).

The EBC analysis carried out over the measurement period for the sites Nazinga, Kayoro, and Sumbrungu revealed EBC gaps ranging from 10 to 30%. Nazinga had the highest coefficient of determination at 0.88, indicating a more consistent EBC, while Sumbrungu had the lowest at 0.85. With intercept values of 18.3 for Nazinga, 8.3 for Kayoro, and 24.6 for Sumbrungu, and corresponding slope values of 0.81, 0.68, and 0.66, the data suggest the best energy balance performance at Nazinga (Figure 5). This indicates that the EBC is the best in the natural site of Nazinga, worse in Sumbrungu and worst in Kayoro. This might be due to the higher heterogeneity of the landscape around Kayoro and Sumbrungu compared to that at the Nazinga site. Here, the surrounding vegetation canopy is much more homogenous compared to the other sites, which may cause turbulent structures that are better recorded by the EC method. A study by Stoy et al. (2013) across Fluxnet sites in 173 ecosystems shows, that landscape-level heterogeneity is negatively related to EBC. Also, Foken (2008) state that surface heterogeneity enhances buoyancy-driven turbulences. It further causes large-scale eddies that cannot be captured by a single EC tower with an half-hourly averaging period due to their size and slow motion and therefore leads to a bigger EBC gap (Kanda et al., 2004; Foken et al., 2011; Eder et al., 2014; de Roo and Mauder, 2018). Quansah et al. (2015) obtained very similar EBC results for the first year of the EC measurements. Their regression fits resulted in a coefficient of determination of 0.92 in Nazinga, 0.90 for Kayoro and of 0.89 for Sumbrungu. The slopes and intercepts were 0.89 and 9.85, 0.67 and 11.34, and 0.67 and 32.60 for the three sites, respectively, (Quansah et al., 2015). Thus, they were slightly higher than those in the analysis conducted here, which indicates that the EBC for the first year of measurements was better than for the time periods analyzed in this study. This suggests that throughout 2013 the meteorological conditions for EC measurements (stationary and turbulent transport) were slightly better than in the other years (2014–2016). Seasonal and CP-dependent energy balance closure.

We examine the EBC additionally for four monsoon seasons and for the different CPs by computing different performance measures for these sub-classes (Supplementary 1, 2). Figure 6 shows the regression fits of the EBC exemplarily for CP4 (typical for the monsoon phase) and CP6 (typical for the dry phase). The quality of the flux measurements is relatively high for the different seasons and CPs with coefficient of determination values ranging between 0.84 and 0.88. The scatter plots also indicate that there are differences in EBC for the wet and dry CPs. This effect becomes much clearer when calculating relative values of the two bias measures and relating them to the wetness index of the CPs (Figure 7). There is a tendency that the EBC (in terms of the mean and variance) is better for the rainy (high WI) than for the dry season (low WI). However, in the case of Nazinga, a slight overestimation of the fluxes occurs during the dry season. Quansah et al. (2015) suggest that the EBC can be affected by changes in the meteorological conditions prevalent during the dry and rainy season. Dust accumulation on the sensors, which affects the measurements, is a possible reason for the positive bias (B₁) in the dry season in Nazinga, as itis located in a natural reserve and not maintained as regularly as the other two sites. Bagayoko et al. (2006) also found that the sensitivity of the measurement system to dust and raindrops has a significant effect on the reliability of EC measurements in this region. The overestimation could also be attributed to an overestimation of LE during dry conditions (Liu et al., 2024). Our results stand in contrast to recent findings of Liu et al. (2024), who found that the EBC gap improves over dry soil compared to wet soils due to an overestimated latent heat flux. However, this might be explained by the open-path gas analyzer, as the underestimation of LE under atmospheric conditions with high relative humidity is smaller when using this instrument than when using closed path systems (Zhang et al., 2023).

Moreover, it stakes out that the differences between the biases of the EBCs were greater among the three stations than among the CPs at each station. This leads to the assumption that site factors, and in this case also the land use in which the three sites differ, have a greater impact on the EBC than the atmospheric conditions. Zhou et al. (2019) found that the EBC gap increases with surface heterogeneity, as long as the heterogeneity scale is smaller than the boundary layer height. As the landscape in the studied areas becomes heterogeneous at quite small scales (Bliefernicht et al., 2018), this strengthens our argument. Further, not only the mean but also the variance of the turbulent fluxes is too low. This underestimation is even more pronounced in terms of relative values for each site as illustrated in Figure 6.

All post-closure approaches reduce the underestimation of the turbulent fluxes leading to a regression slope closer to 1 (Figure 8). The slope of the regression line improved significantly, with an enhancement by approximately 33–40%, particularly at sites where the underestimation was most pronounced. However, the scatterplots alone do not reveal clear distinctions between the performances of the three post-closure approaches. For a closer look at the quality of the correction methods for the different monsoon phases, we determine B₁ and B₂ for each CP (Figure 9). All post-closure approaches can reduce the strong biases for the different WAM phases (Table 3). However, in many cases the BR correction does not lead to a full reduction of the biases. In several cases, new overestimates are introduced, especially for the B₁-values at Sumbrungu (Figure 9e), but also for several CPs at the other sites, which were even higher than the original bias (e.g., CP1, CP6 and CP7 for the mean of Nazinga, Figure 9a). We find a similar pattern looking at the relative bias measure RB₁ (Supplementary 3). This indicates a clear limitation of this methodology. A potential reason might be the overestimation of evapotranspiration, as pointed out by Mauder et al. (2018) in a study of two grassland sites. As Finnigan et al. (2003) and Mauder and Foken (2006) have shown that the energy balance closure can be improved with a higher averaging time. Furthermore, Wohlfahrt et al. (2009) suggest adjusting the energy balance closure (EBC) using a longer-term (i.e., monthly) correction factor. However, our analysis (not shown) shows that applying the Bowen ratio method with a monthly correction factor does not improve the results compared to using daily hourly corrections across the different EC sites.

The correction of the turbulent fluxes with the QM method achieves a further reduction of both bias values in most cases compared to the BR method. In contrast to the BR method, a correction of the entire distribution function is performed, minimizing any systematic deviations from the mean and variance and therefore outperforming the BR method. However, the outcomes in Figure 9 also show that significant biases of the turbulent fluxes remain for certain CPs if the QM method is used. After performing the bias correction for each CP using the QM-CP approach, the bias is even further reduced for each CP and no longer visible in the chart. Thus, the post-closure approach based on the empirical distribution function of the turbulent fluxes conditioned on the monsoon phases outperforms the other methods. The overall performance measures CB₁ and CB₂ confirm this (Figure 10). With the QM-CP correction, CB₁ and CB₂ are almost fully eliminated (with values between 0.02 and 0.1 W/m²). Therefore, the novel QM-CP method performs best in comparison to the other two correction methods.

We further use the post-closure approaches to generate corrected partitioned sensible and latent heat fluxes to analyze the impact of the bias correction methods on both. Figure 11 shows the corrected and uncorrected fluxes for 3 days in the rainy season (July 20th–23rd 2014) for the sites where the underestimation of the turbulent fluxes was strongest (cropland site at Kayoro) and weakest (near-nature site at Nazinga). In the rainy season, LE is usually distinctly higher than H compared to the dry season (Timouk et al., 2009). It is noticeable that all correction methods preserve the diurnal cycle of the turbulent fluxes for the different sites and lead to no obvious outliers due to the correction. The QM approaches lead to higher H during the day at both sites, especially over midday, while the BR method leads to a lower H compared to the original time series. LE is increased by all approaches, at the natural site to a similar degree across methods, at the cropland site the quantile mapping approaches increase it more than the BR correction at two of the 3 days.

The time series examples (Figure 11) clearly show that the typical diurnal cycle of the turbulent fluxes can be preserved by all applied post-closure approaches. However, there are strong differences regarding the magnitude and orientation of the corrected turbulent fluxes, leading to significant differences in comparison to the original and corrected measurements for specific days and diurnal periods (noon). The difference between the QM approaches is not very large as the bias reduction due to the introduction of the CPs is minor as shown in the previous section.

There are also several possibilities for a further advancement of the post-closure methods. Especially, the adjustment factor (EF) used for the partitioning of the residuals should be explored in more detail in future. For instance, Mauder et al. (2018) found that a daily adjustment factor leads to less scatter in the evapotranspiration than sub-hourly factor as chosen for the quantile-mapping approaches in this study. To keep the scatter in the corrected data on a lower level, the EBC adjustment factor should be determined for longer periods as already proposed by Mauder et al. (2013). This can be done for each CP by determining a mean diurnal profile for EF which can then be used for partitioning the turbulent fluxes. There is a controversial discussion about the diurnal constancy of EF, the “daytime self-preservation” (Gentine et al., 2007). In many experimental conditions, the EF is found to be stable during daylight hours (Shuttleworth, 1991; Nichols and Cuenca, 1993; Crago, 1996). However, various studies question that. Although Lhomme and Elguero (1999) confirmed that in conditions of “fair weather,” the curve representing the diurnal course of EF has a typical concave-up shape and appears relatively constant around mid-day, they have shown that it is not necessarily constant during daytime especially in “non-fair weather conditions.” Thus, determining a mean profile for EF for different weather conditions (or circulation patterns) seems to be relevant and the corresponding impact of choosing this profile for an adjustment of the turbulent fluxes needs to be explored in future studies in more detail.

In order to check whether the corrections have a positive effect on the ascertainment of the latent heat flux and therefore evaporation, the results of this study should be verified with independent reference datasets. One option is the comparison with highly precise lysimeter estimates of actual evapotranspiration to identify practical approaches for a correction of the energy fluxes (Gebler et al., 2015; Wohlfahrt et al., 2010). Mauder et al. (2018) performed these comparisons with EC measurements from two grassland sites in southwestern Germany within the TERENO (Terrestrial Environmental Observatories) network. However, this type of measurement is not (yet) available for the sites examined in this study. A further option is integrated numerical modeling of the relevant land surface processes, as it provides useful insights about the possible partitioning of the energy balance residuals into sensible and latent heat fluxes (Ingwersen et al., 2011). In future the use of machine-learning techniques could also be useful in this context. Zhang et al. (2023) have applied such method to correct the LE in conditions of high relative humidity (>70%). They emphasize the potential underestimation of ET and LE during such conditions as source of uncertainty, which is often not characterized. The outcome was compared to LE corrections based on the BR methods and to the total LE attribution of the residual.