The modelling approach used for the vegetation canopy is an important feature that influences how the soil and vegetation interact. Depending on the approach used, Ts, qa, Ra will evolve differently and ultimately influence evapotranspiration. In many LSMs, the strategy for modelling the vegetation canopy is to include it in the top surface layer which is then referred to as the composite layer because it mixes soil and vegetation properties . This composite approach considers only one temperature and soil moisture for the composite layer, with properties such as thermal inertia or conductivity that may vary depending on the proportion of vegetation in the composite layer. There is only one surface temperature Ts and the atmospheric environment is the same for the vegetation and the ground.The total evapotranspiration, ET, is then the sum of the vapour fluxes from the vegetation transpiration Etr and the bare ground Eg: 4ET=fvegEtr+1-fvegEg where fveg is the fraction of vegetation covering the surface. This composite approach is still used in many Numerical Weather Prediction (NWP) systems due to its simplicity and low computational cost . However, this simplicity comes at the expense of realism, and the composite approach may yield unrealistic amounts of bare ground evaporation or overestimate the surface soil temperature for large LAI values .

The strategy to overcome this issue is to separate the modelling of the soil and of the vegetation . This strategy is often called Two-Source Energy Balance (TSEB) in LSMs and is called Multi Energy Balance (MEB) in ISBA since it also potentially includes a separate snow surface energy budget.

For the current study, it computes two separate Surface Energy Balance (SEB) for the ground and the vegetation, the atmospheric properties are discretized in the vertical in the canopy, meaning that Ra and qa are computed separately for the canopy (giving Ra–c and qa, c) and for the ground (Rc-g and qa, g), and the temperature of the canopy and the ground are resolved separately, giving Ts, c and Ts, g instead of a single surface temperature Ts. Transpiration Etr and bare ground evaporation Eg both participate in modifying the atmospheric properties at the canopy level, and total evapotranspiration is then calculated as the vapour flux between this canopy atmosphere and the overlying atmosphere. The full set of equations used in MEB is described in , but is not detailed here for the sake of brevity.

The surface resistance Rs (Eq. ) is a key variable for modelling the response of the plant to external conditions. This surface resistance is actually mainly determined by the aperture of the leaf stomata and is therefore often referred to as stomatal resistance. It will be referred to as such in the remainder of this work. Stomatal conductance gs, the inverse of stomatal resistance, is also often used in the literature. Stomatal conductance gs can be modelled using several approaches, two of which are used in ISBA: Jarvis and A-gs schemes .

The Jarvis parameterization is rather simple and aims at modelling only vapour fluxes. Stomatal conductance in this case is mainly a function of incoming radiation, soil water stress, Vapour Pressure Deficit (VPD), air temperature and a few plant characteristics. In the Jarvis parameterization, the influence of each parameter is independent of the others.

The A-gs schemes are more recent parameterizations that model the photosynthetic and transpiration processes more realistically, based on the work of . It allows the carbon exchange between vegetation and the atmosphere to be modelled explicitly, as well as the interdependence between the parameters already considered in the Jarvis scheme. It has been adapted to ISBA in the so-called ISBA-A-gs scheme by . The Jarvis and A-gs stomatal conductance parameterizations are common to many LSMs .

Irrespective of the stomatal conductance parameterization chosen, vegetation characteristics also play a role in determining the stomatal conductance, gs. In particular, the response of plants to water stress is an important feature to consider in ISBA. and identified two categories of responses under moderate stress, drought tolerance and drought resistance. The drought-tolerant strategy of a plant is to facilitate transpiration in order to increase the evaporative cooling effect, which also leads to a decrease in the photosynthetic carbon assimilation rate. In the drought-avoidance strategy, the plant is more likely to close its stomata when leaf surface temperature Ts is too high or specific humidity qa is too low, in order to reduce transpiration and water loss. Under severe water stress, both strategies lead to a large decrease in stomatal conductance and thus transpiration.

The last parameter tested for its influence on evapotranspiration is soil moisture. It is essential as it directly influences plant transpiration Etr by modulating Rs through plant water stress and soil evaporation Eg through hu, which is a function of soil moisture through Eq. (). 5hu=0.51-cos⁡wgwfcπifwg≤wfc1ifwg≥wfc To allow comparison of soil moisture values across different soil textures, the Soil Wetness Index (SWI) is often used in LSM parameterizations and is also used in this article. The SWI is defined by the Eq. (). 6SWI=wg-wwiltwfc-wwilt where wg is the volumetric soil moisture, wwilt is the volumetric soil moisture at the wilting point, and wfc is the volumetric soil moisture at field capacity, all in m³ m⁻³. A SWI value of 0 means the soil is at wilting point, and a value of 1 means the soil is at field capacity. Very dry soils may have negative values, and wet soils may have values greater than 1, up to saturation. At wilting point the plant cannot extract water from the soil and transpiration drops to zero. At field capacity, the soil moisture does not limit the plant transpiration. The transpiration is then limited by other factors (incoming radiation, temperature, CO₂ concentration, …).

In order to assess the behaviour of the modelled evapotranspiration in different configurations, the parameters discussed above are all tested with different fixed SWI values. These fixed values allow the effect of different levels of water stress on transpiration to be clearly identified. In addition to the fixed SWI runs, ISBA is also run in its standard mode, with an evolving soil moisture without irrigation (NOIRR), and with irrigation parameterizations. The first parameterization keeps the soil at field capacity and is called IRR_FC. NOIRR and IRR_FC are used in both coupled and offline simulations. Another type of irrigation parameterization is used in the offline simulations since it is also commonly used in the literature . These parameterizations add 30 or 100 mm of water to the top soil layer when the SWI falls below the 0.5 threshold. They are called IRR_THLD.

Between 14 and 30 July 2021, the observed and modelled mean diurnal cycles of near-surface air temperature are shown in Fig.  for the locations of the IRTA corn field and La Cendrosa alfalfa field sites. For clarity, only the mean diurnal cycles are shown in the main body of the article. However, the full time series over the SOP can be found in Appendix . The difference between the coupled simulations IRR_FC and NOIRR allows quantification of the mean cooling effect of irrigation, which is found to range between -1.5 and -3 °C for the modelled 2 m air temperature, depending on the time of the day. The cooling effect of irrigation significantly reduces the discrepancy between observations and the simulated results from the IRR_FC coupled run.

In the morning, between 06:00 and 09:00 UTC over the IRTA corn field (Fig. a), the coupled simulation with irrigation manages to accurately model the air temperature. During afternoons and nights, this coupled simulation moves away from the observations. This behaviour suggests that the model has inherent biases that vary over the course of the day, and that the overestimation of air temperature by the coupled simulation IRR_FC during the afternoon and night is not due to a misrepresentation of irrigation effects, as it is well represented in the morning.

Over the alfalfa field of La Cendrosa (Fig. b) the modelled cooling effect is slightly more important than over the IRTA corn field. It is about -3 °C throughout the day. The remaining overestimation of air temperature by the model IRR_FC compared to observation is relatively constant throughout the day. It is about 1 °C during the day and about 1.5 °C during the night. For the La Cendrosa alfalfa field, as for the IRTA corn field, the remaining overestimation of the night air temperature by the IRR_FC simulation is most likely due to the difficulty of the model to represent the stable conditions of the night .

The performance scores of the coupled model runs with and without irrigation are shown in Tables  and , for the IRTA corn field and the La Cendrosa alfalfa field, respectively. The scores are given for daytime, as it is mainly the daytime values that influence evapotranspiration, and also for the whole period to give a general view of the model behaviour. The average cooling effect of irrigation over the whole period is -2.21 and -2.65 °C for the IRTA corn field and the La Cendrosa alfalfa field, respectively, and -2.40 and -2.87 °C for the daytime only.

The remaining temperature bias found between the IRR_FC coupled simulation and the observations depends on the day. showed that for 21 and 22 July 2021, adding irrigation to the coupled model causes a reduction in most of this bias, but for some other periods the bias is higher. This may be due to the fact that even if the activation of irrigation improves the model representation of winds, some wind regimes may be missed. As the topography of the region is complex, it is expected that the models do not capture all of the mesoscale winds . In addition, the coupled model has inherent biases, which may be related to the modelling of stable atmospheric conditions, the composite approach used in SURFEX, biases in meteorological variables derived from analyses used at the boundaries of the simulation domain, or potential misrepresentation of the land surface in the vicinity of the Urgell area. In particular, the vegetation in the model around the irrigated area may have too shallow roots as discussed by and , leading to an overestimation of plant water stress and ultimately to warmer air. The precise characterization of the internal model biases in this region would require extensive further work, which is considered beyond the scope of the current study. showed that irrigation parameterizations that maintain SWI values within irrigated areas close to field capacity perform very well. Therefore, in the context of this work, it is assumed that the remaining overestimation of air temperature is not due to a misrepresentation of the irrigation effect, but to other shortcomings of the model.

The mean effect of irrigation on near-surface specific humidity is shown in Fig. . In the IRR_FC coupled simulation, the mean specific humidity over the IRTA corn field is overestimated throughout the day (Fig. a). The overestimation is specifically important at 08:00 UTC, reaching up to 2 g kg⁻¹. This overestimation of humidity in the morning is due to the lack of vertical mixing in the lower ABL, as already discussed in . During the afternoon, the simulation IRR_FC reduces the discrepancy with the observation, although it still overestimates the absolute value. The difficulty of the simulation in modelling the specific humidity at the IRTA corn field could be due to several shortcomings of the coupled model, such as the misrepresentation of the neighbouring town of Mollerussa or the overrepresentation of irrigated areas in the immediate vicinity of the IRTA corn field. In any case, the difference between the simulations NOIRR and IRR_FC allow an estimation of the humidifying effect at the IRTA facility, and it is found to be +2.31 during daytime, and +1.50 g kg⁻¹ globally (Table ).

At the La Cendrosa alfalfa field, the specific humidity during the day is well modelled by the simulation IRR_FC as shown in Fig. b. At night, the specific humidity is slightly underestimated, probably due to the difficulty of the model in modelling stable nighttime conditions as discussed above. At all times the simulation IRR_FC improves the underestimated humidity of the simulation NOIRR. The humidifying effect at La Cendrosa is found to be +2.68 during daytime, and +1.78 g kg⁻¹ globally (Table ).

Many studies have shown that irrigation can slow the wind near the surface . This is also the case in the Urgell region, as shown in for the 21 and 22 July, and in Fig.  for the whole SOP at the two observation sites. The mean reduction in wind speed due to irrigation is -0.60 and -0.68 m s⁻¹ for the corn and alfalfa fields, respectively, during the SOP (Tables  and ). During the day only, the reduction in wind speed due to irrigation is -0.86 and -0.94 m s⁻¹, respectively. This reduction in wind speed is mainly due to the reduced momentum flux between the free troposphere and the surface .

However irrigation can also influence the dynamics of mesoscale winds which are modulated by the complex topography of the Urgell region . In particular, the Marinada is the mesoscale wind that blows strongest during the SOP. It corresponds to the peak wind speed found at 17:00 and 19:00 UTC for the NOIRR and IRR_FC coupled simulations in Fig. a and b, respectively. In particular, both figures show that the peak wind speed is delayed by irrigation and that the maximum wind speed is significantly reduced by up to 1.4 m s⁻¹, thus confirming the findings of over the longer period of the LIAISE SOP.

The reduction in wind speed due to irrigation allows a more accurate representation of the wind speed in the coupled model compared to observations. Fig. b shows that the irrigated coupled simulation IRR_FC performs very well in representing the wind speed at the La Cendrosa alfalfa field. The irrigation parameterization also improves the representation of wind speed over the IRTA corn field, but some biases remain. Figure a shows a relatively poor agreement between the irrigated simulation and the observations for the IRTA corn field, especially for the evening and night. Since the modelled wind speed behaviour is very similar in the IRTA corn field as in La Cendrosa, the reason for the poor agreement is more related to the observed wind speed pattern of the IRTA corn field, which is different from that of La Cendrosa mainly because it does not show faster winds between 16:00 and 20:00 UTC, which should correspond to the Marinada. A possible explanation for this is the organization of crop canopies into rows in and around the corn field. As shown by , the angle between the rows and the wind can influence the wind speed up to two times the canopy height. This is the case for the corn field where the wind speed sensor is located at 3.6 m a.g.l., in a 2 m wide linear corridor between two rows of corn, with a surrounding canopy at 2.3 m. The rows of corn and most of the surrounding crops are aligned on a southwest-northeast axis. This is almost parallel to the dominant west-southwest wind that blows in the Urgell region, and therefore the crops offer less resistance to the wind coming from this direction. Conversely, the Marinada is a southeasterly wind that is almost perpendicular to the rows, which means that the measured wind may be weaker. In other words, the west-southwest wind sees a relatively lower roughness length than the southeast wind. However, the effect found by is relatively small, about 0.1 to 0.2 m s⁻¹ at 1.7 times the canopy height. Although the field studied in is not the same, it is delicate to assume that all the bias between the observations and the irrigated simulation comes from the observational data. In conclusion, the reason for the absence of the Marinada signal in the wind speed measurements over the corn field would require other types of observations and an in-depth investigation, which is not undertaken in the present work.

This section confirms the strong influence of irrigation on air temperature, humidity and wind speed, and quantifies these effects during the LIAISE SOP with surface–atmosphere coupled simulations. Although the coupled model proves to be able to represent well this influence, it is also shown that biases remain between the model with irrigation and the observations. This could be due to problems inherent in the model or also to some measurement uncertainties. For the remainder of this study, it is assumed that among the various potential model shortcomings, the remaining biases are not so much due to misrepresentation of irrigation effects, but rather mostly to other model shortcomings.

One can rightly argue that the two weeks of the LIAISE SOP may not fully represent the entire irrigation period. Nonetheless, this SOP was selected for study in the present work due to the computational intensity of the coupled land-atmosphere model and the fact that most of the LIAISE atmospheric observations were available during this time, facilitating the validation of model outputs. Quantifying the irrigation-induced atmospheric effects outside of this SOP is challenging due to the absence of two coupled models differing solely by the presence or absence of irrigation. However, the representativeness of the SOP relative to the full irrigation period can be assessed globally through indirect methods. To this end, the ERA5 database can replace the NOIRR simulation. ERA5 is a global reanalysis, obtained with the surface-atmosphere coupled model of the European Center for Medium-range Weather Forecast (ECMWF), run with a horizontal resolution of 31 km and no irrigation parameterization. However, replacing the IRR_FC simulation with another weather simulation product is not feasible since no NWP or reanalysis operational model currently represents irrigation. Therefore the local near-surface observations are used to represent the IRR_FC simulation. For example, the meteorological station at La Cendrosa operated throughout the entire LIAISE Long Observation Period (LOP), which extends from mid-April to mid-October 2021. Appendix  illustrates the atmospheric effects of irrigation evaluated over the five months of the LIAISE LOP using ERA5 data and observations, as well as the two simulations NOIRR and IRR_FC. Firstly, it can be seen that the atmospheric effects induced by irrigation over the two weeks of the SOP are similar when obtained using the two simulations or using the observations and ERA5. The cooling effect is found to be about -3.0 °C in both cases. The humidifying and wind speed reduction effect are about +1.9 g kg⁻¹ and -1.0 m s⁻¹ (based on ERA5-observations datasets), and +2.8 g kg⁻¹ and -1.5 m s⁻¹ (based on high-resolution simulations). The small discrepancy in irrigation effect obtained using the two simulations or using the ERA5-observations datasets may be due to the coarse resolution of the ERA5 model. For instance, the coarse horizontal resolution does not enable mesoscale winds to be represented. Nevertheless, the magnitudes of the irrigation effects on the atmosphere are similar, suggesting that the differences between the ERA5 reanalysis and the observations adequately capture the atmospheric effects of irrigation. Therefore these datasets can be used to evaluate the temporal variability of this effect. Over the LOP, the irrigation atmospheric effect appears to be quite pronounced and relatively stable on average from early June to late August. Thus, this study, which focuses on the two-week SOP, is not an exceptional case but can instead be considered representative of the summer irrigation period.

This section aims to better understand the ISBA processes that regulate evapotranspiration under different atmospheric conditions. To focus on the effects of atmospheric conditions, a fixed surface configuration is maintained which includes a single Plant Functional Type (PFT) representing a drought-tolerant crop, a composite approach for the vegetation representation, a stomatal conductance modelled with ISBA-A-gs. The atmospheric forcing used corresponds to the near-surface atmospheric conditions found over the IRTA facility at 2 m a.g.l. in the coupled model runs. The rest of the offline ISBA configuration corresponds to the values presented in Sect. . Note that even though the near-surface atmospheric conditions are those of the IRTA facility, the underlying surface of the offline run is not intended to be representative of the actual IRTA corn field. This allows the effect of atmospheric feedback on evapotranspiration to be isolated from the effects of surface characteristics on evapotranspiration.

When a crop is well irrigated, most of the evapotranspiration is driven first by incoming (downward) shortwave radiation and secondly by air temperature, humidity and wind. On 15 July 2021, no clouds were modelled in Meso-NH, and therefore the incoming shortwave radiation was essentially the same in the two atmospheric forcings atmo_IRR_FC and atmo_NOIRR. Thus, for the two offline ISBA runs, the factors for the differences in evapotranspiration are found in air temperature, humidity and wind.

Figure  shows the different atmospheric conditions from the two atmospheric forcing dataset for 15 July 2021 at the IRTA facility, and the resulting evapotranspiration modelled by the offline ISBA. The point-scale offline ISBA simulation has a SWI = 1.0. The cumulative evapotranspiration modelled with the atmo_NOIRR atmospheric forcing, i.e. with a warm, dry, and windy atmosphere, is 21 % higher than that produced with the atmo_IRR_FC atmospheric forcing. In other words, all other things being equal, neglecting the irrigation effect in the atmospheric forcing leads to a 21 % overestimation of evapotranspiration for 15 July 2021. This corresponds to an overestimation of the daily mean latent heat flux by 36 W m⁻², or an overestimation of the cumulative daily evapotranspiration by 1.37 mm d⁻¹.

In irrigated regions, not all crops are necessarily irrigated. These rainfed crops are therefore exposed to atmospheric conditions influenced by irrigation without being irrigated themselves. In this case, the plant may be under water stress and may close its stomata to limit water loss. As stomatal closure is controlled not only by soil moisture but also by temperature, specific humidity and wind speed, the atmospheric feedback also affects stomatal closure, and eventually transpiration. Note that stomatal closure is also controlled by shortwave radiation and CO₂ concentration, but these effects are neutralized in the present study as discussed previously.

Figure  shows the transpiration modelled by offline ISBA for two different days, for a SWI value of 0.2, and with the two different atmospheric forcings atmo_NOIRR and atmo_IRR_FC at the IRTA facility. On 18 July (Fig. a), the temperature is higher than for the 15 July conditions shown in Fig. , and the model represents stomatal closure for the simulation with the atmo_NOIRR atmospheric forcing. The stomatal closure is characterized in the time series of transpiration vapour flux by a sudden drop in the flux value found during the day. On 18 July, the stomata close between 12:00 and 15:00 UTC, when the air temperature is highest. The asymmetry of stomatal closure around midday confirms the strong effect of air temperature. Conversely, no stomatal closure is modelled for the simulation using the atmo_IRR_FC atmospheric forcing. In this case, the atmospheric feedback, i.e. the cooling, humidifying effect and the weakening of the wind, prevents stomatal closure. Counter-intuitively, the cumulative transpiration for this day is higher for the simulation with the atmo_IRR_FC atmospheric forcing, i.e. with cooler, more humid and less windy atmospheric conditions. The simulation with atmo_NOIRR underestimates the transpiration rate by 29 % compared to the simulation with atmo_IRR_FC. This corresponds to an underestimation of the daily mean transpiration latent heat flux by 30 W m⁻², or an underestimation of the cumulative daily transpiration by 1.14 mm d⁻¹.

On a hotter day like 22 July 2021, both simulations show stomatal closure (Fig. b). However, the atmospheric feedback still allows stomata to close later in the morning. The simulation with the atmo_IRR_FC atmospheric forcing has stomatal closure between 12:00 and 15:00 UTC, while the atmo_NOIRR forcing results in stomata closure between 10:00 and 14:30 UTC. Somewhat unexpectedly, stomata reopen earlier in the case without atmospheric feedback. This is due to the earlier arrival of the Marinada in the atmo_NOIRR atmospheric forcing, as shown by . This behaviour is therefore specific to the region of the present case study and cannot be extended to other regions of the world. Without the Marinada delay, the atmospheric feedback should have led to an earlier reopening of the stomata. The daily transpiration difference is again negative, meaning that the atmospheric feedback led to higher transpiration rates. The offline simulation with atmo_NOIRR atmospheric forcing, i.e. without atmospheric feedback, underestimates the transpiration rate by 10 %. This corresponds to an underestimation of the daily mean transpiration latent heat flux by 7 W m⁻², or an underestimation of the cumulative daily transpiration by 0.28 mm d⁻¹.

However, transpiration is only part of evapotranspiration, the other consisting in evaporation from the bare ground (there is no water intercepted on the leaves). The total evapotranspiration is shown in Fig. . Stomatal closure can still be seen in the daily evolution of total evapotranspiration, however, the decrease in total evapotranspiration is not as significant as for transpiration only.

On 18 July at 13:00 UTC, the instantaneous decrease due to stomatal closure for transpiration only is about 220 W m⁻², while the decrease for evapotranspiration is about 100 W m⁻². The difference in the magnitude of the decrease between transpiration and evapotranspiration is due to a compensating effect of bare soil evaporation. In the composite approach, as vegetation transpiration decreases, more heat is available to the composite layer, and the soil responds quickly by increasing its temperature. In the separate canopy approach of MEB, as transpiration decreases, the canopy converts more radiative energy into thermal energy, increasing the canopy air temperature and also the top soil temperature. Under either approach, the soil warms as transpiration decreases and evaporation from the bare soil increases in response.

Another interesting effect due to evaporation can be seen in Fig. . Soil evaporation is also more sensitive to wind speed than transpiration, and evaporation peaks when the sustained wind speed of the Marinada arrives. Combining Eqs. () and (), it can be observed that the ISBA LSM formulates evaporation as proportional to wind speed Va, while transpiration is also modulated by stomatal resistance Rs, leaf. This strong dependence on the wind speed allows the modelled evapotranspiration to reach up to 615 W m⁻² (0.98 mm h⁻¹) on 22 July at 15:00 UTC when the Marinada arrives. In this case, it is important to consider the role of the irrigation-induced decrease in wind speed. The excessively windy atmospheric forcing atmo_NOIRR leads to an overestimation of the mean evaporation up to 63 % and 47 % for 18 and 22 July, respectively (Appendix a, b). These values correspond to an overestimation of the daily mean evaporation latent heat fluxes by 41 and 47 W m⁻², or an overestimation of the cumulative daily evaporation by 1.54 and 1.80 mm d⁻¹. By aggregating the role of evaporation and transpiration, for the days shown in Fig. , it can be found that the atmo_NOIRR atmospheric forcing leads to an overestimation of evapotranspiration by about 6 % and 23 % for 18 and 22 July, respectively, corresponding to an overestimation of the daily mean latent heat fluxes by 10 and 39 W m⁻², or an overestimation of the cumulative daily evapotranspiration by 0.40 and 1.52 mm d⁻¹.

It should be noted that these results are obtained using the composite approach to vegetation representation, which is known to have limitations with respect to bare ground evaporation . By using the MEB option, the wind speed seen by the ground surface can be modelled more realistically and is significantly lower than that seen by the canopy. The MEB approach also takes into account the sheltering effect of the canopy and the temperature of the top layer of soil is independent of the canopy temperature. This more realistic approach means that ISBA does not compensate for reduced transpiration by increasing evaporation as much as in the composite approach. The overestimation of evaporation then decreases, becoming negligible on 18 July, but remaining on 22 July. The mean evaporation is overestimated by 0.5 % and 17 % for 18 and 22 July, respectively (Appendix c, d). These values correspond to an overestimation of the daily mean evaporation latent heat fluxes by 1 and 11 W m⁻², or an overestimation of the cumulative daily evaporation by 0.01 and 0.43 mm d⁻¹. With the separate canopy approach of MEB, the behaviour of total evapotranspiration is closer to that of transpiration. On 18 July the evapotranspiration is underestimated by 16 % (24 W m⁻² or 0.92 mm d⁻¹), whereas on 22 July it is overestimated by only 5 % (6 W m⁻² or 0.24 mm d⁻¹).

Note that the atmospheric feedback on evaporation and the compensation effect must be interpreted with caution. Evaporation from bare soil is strongly dependent on the top soil humidity hu. Although moisture can be evaporated from the soil for soil moisture below the wilting point, i.e. for SWI<0, the rate of evaporation will be low for such dry soils. Note that the model configuration used in Fig.  is conceptual and keeps SWI at a value of 0.2, which allows the top soil layer to be moist enough to provide a significant evaporation rate throughout the simulation. In reality, or in a more realistic flood irrigation parameterization, the top soil layer would dry out and evaporation could not compensate as much for the decrease in transpiration. Although the magnitude of the evapotranspiration compensation effect is uncertain, it is important to consider this process when interpreting the evapotranspiration outputs of LSMs in different configurations, as is done in the next section.

The previous sections have shown that for equal incoming shortwave radiation, the atmospheric feedback is particularly important to consider in offline ISBA simulations. For well-irrigated plants, the atmospheric feedback is shown to reduce modelled transpiration and evaporation. For water-stressed plants, however, more complex processes are involved. The atmospheric feedback has a clear influence on the timing of stomatal closure, which can compensate for the decrease in transpiration or even lead to the opposite effect, i.e. an increase in transpiration. It has also been shown that transpiration and soil evaporation are not separate processes, but interact with each other through surface temperature. More specifically, a decrease in transpiration leads to an increase in bare soil evaporation in the ISBA LSM.

The previous section explored and quantified these processes for specific days and for a few ISBA configurations. A more systematic assessment of the effect of atmospheric feedback on vapour fluxes is still needed. For this purpose, the overestimation of evapotranspiration due to the atmo_NOIRR atmospheric forcing is quantified for the different offline ISBA configurations presented in Table . The influence of the different parameter combinations is also discussed in the light of the previously presented processes. Note that the combinations of soil moisture and different atmospheric conditions presented are realistic. Although irrigation has a significant impact on near-surface atmospheric conditions, synoptic conditions remain the primary driver of atmospheric properties. Consequently, under conditions with sufficiently strong horizontal advection, it is possible to have a hot, dry atmosphere above a small irrigated area with wet soil, or conversely, a non-irrigated parcel with dry soil in the middle of an irrigated area with a relatively cool, humid atmosphere.

Figure  shows the overestimation of transpiration and evaporation rates modelled by ISBA for different soil moisture values, different ISBA configurations (listed in Table ) and for two different locations in the irrigated area of LIAISE. Soil moisture levels are represented by SWI because it is the main moisture control factor for transpiration in the ISBA model. Also evaporation is controlled by the ratio Wg/Wfc, which is conceptually similar to SWI (cf. Eq. ). The SWI remains constant throughout each simulation, meaning that the same SWI levels impact transpiration and evaporation in Fig. . Note that these idealized constant SWI values are used here to analyze the sensitivity of transpiration and evaporation to soil moisture. In the realistic parameterizations IRR_THLD (described in Sect. ), the topsoil layer dries out quickly while the root zone remains wet for a longer period of time.

For transpiration, the absolute value of the overestimation is highly dependent on the soil moisture and the stomatal conductance scheme (Fig. a and c). With Jarvis, the mean absolute overestimation of transpiration due to the lack of atmospheric feedback ranges between 28 and 56 W m⁻² (1.07 and 2.14 mm d⁻¹) for wet soil where SWI≥1. In relative terms, these values correspond to a 19 % to 35 % overestimation of the mean transpiration vapour flux. For dry soil (SWI=0.1) the overestimation ranges from 1 to 21 W m⁻² (0.04 to 0.80 mm d⁻¹), corresponding to a relative overestimation of 4 % to 21 %. No value is shown for SWI=0 as the modelled transpiration is zero. For these drier soils and with Jarvis, the decrease in the absolute value of the overestimation is due to the overall decrease in evapotranspiration, but also partly to the compensating effect of stomatal closure as presented in the previous section. Stomatal closure/opening is regulated by stomatal conductance and the associated scheme. Figure a and c show that the Jarvis scheme leads to higher overestimation of transpiration than the ISBA-A-gs scheme. In fact, the Jarvis scheme does not model rapid stomatal closure. Instead, it gradually reduces stomatal conductance during the day and leads to a weak compensation effect with respect to the timing of stomatal closure (not shown).

In contrast, when the ISBA-A-gs scheme is used, stomatal closure compensation is more significant and greatly reduces the overestimation of transpiration for all soil moisture compared to the Jarvis scheme. For ISBA-A-gs and wet soils, the lack of atmospheric feedback can lead to either an overestimation of 14 W m⁻² (0.54 mm d⁻¹) or an underestimation of -12 W m⁻² (-0.46 mm d⁻¹). This can be explained by the fact that the two weeks modelled for the present study are hot and dry in midsummer and therefore the modelled plants often close their stomata when the atmo_NOIRR atmospheric forcing is used, i.e. when it does not include the atmospheric feedback. However, the atmo_IRR_FC atmospheric forcing allows for more days without stomatal closure to be modelled. On these days the atmospheric feedback actually allows a higher cumulative transpiration rate, as shown in Fig. . In the present case, the ISBA-A-gs scheme used with hot and dry atmospheric conditions leads to a low or negligible overestimation of transpiration.

The response of evaporation to ISBA configuration and soil moisture is different from that of transpiration. Figure b and d show the mean absolute overestimation of evaporation as a function of soil moisture. The canopy representation is the main factor to consider in this case, with a higher overestimation when the composite approach is used. With the composite approach, the absolute overestimation values range from 26 to 63 W m⁻² (0.99 to 2.40 mm d⁻¹) depending on the combination of stomatal conductance scheme, drought response and location. The reason for this is the dependence of evaporation on the temperature of the top soil layer. As the top soil layer is a composite layer, its temperature depends on the cooling caused by transpiration. The lower the transpiration, the higher the top soil temperature and ultimately the higher the evaporation, i.e. evaporation compensates, to a certain degree, for the lack of transpiration. The interaction between transpiration and evaporation through surface temperature (either canopy or composite skin temperature) means these two processes are necessarily intertwined and must be interpreted together. This dependence on transpiration is confirmed by the fact that the absolute differences in evaporation rate do not vary with the stomatal conductance scheme for SWI=0, i.e. when transpiration is zero. It can also be observed that the highest values of evaporation overestimation are found for ISBA-A-gs, i.e. for the stomatal conductance scheme that models more stomatal closure and overestimates transpiration less.

With MEB, bare soil evaporation is more physical. It has independent temperatures for the canopy and the top soil layer and takes into account the shading effect of the canopy on the soil. The top soil temperature is not influenced as quickly by stomatal closure as in the composite approach, and therefore the evaporation overestimation is globally similar for all soil moisture and ISBA configurations, with values ranging from 8 to 18 W m⁻² (0.31 to 0.69 mm d⁻¹). In relative terms, these values correspond to a 12 % to 38 % overestimation of the mean soil evaporation vapour flux.

In summary, the overestimation of transpiration is highly dependent on the soil moisture and stomatal conductance scheme, while the overestimation of evaporation is more dependent on the canopy scheme. For the composite approach, the higher the overestimation of transpiration in Fig. a and c, the lower the overestimation of evaporation in Fig. b and d.

Figure  shows the distribution of the total relative overestimations of evapotranspiration, for the two weeks modelled, for different ISBA configurations. These configurations differ in the parameterizations used (see Table ) and in the atmospheric effects of irrigation (from La Cendrosa and the IRTA facility). The detailed relative overestimation for each configuration is shown in Appendix . The results are presented separately for different soil moisture categories in offline ISBA: Non-irrigated and Irrigated. The Non-irrigated column corresponds to the NOIRR case and the Irrigated column corresponds to the IRR_THLD and IRR_FC parameterizations, described in Sect. .

When the soil is not irrigated in the offline simulation, the stomatal closure process plays a key role, and the use of atmo_NOIRR leads to weak or negligible average underestimation of evapotranspiration, between -10 % and 2 %, as discussed in Sect. . Moreover, this small relative underestimation corresponds to small absolute values. This means that a field that is not irrigated, but is subject to atmospheric feedback from surrounding irrigated fields, will not reduce its mean evapotranspiration very significantly.

In contrast, the irrigated field is quite sensitive to the atmospheric feedback. In this case, the use of the atmospheric forcing atmo_NOIRR, which does not include the influence of irrigation on the atmosphere, leads to an overestimation of evapotranspiration of between 4 % and 35 %. For the irrigated offline simulations, the low values of evapotranspiration overestimation (<20 %) are all obtained for ISBA configurations using the stomatal conductance scheme ISBA-A-gs, since this scheme allows more stomatal compensation effect (Appendix ). A LSM using the Jarvis stomatal conductance scheme is more prone to overestimate evapotranspiration over irrigated areas.

Evapotranspiration can also be calculated without LSM, for example using a formula such as FAO-56 from Eq. (). This formula implies a wet soil and crops without water stress, thus conceptually representing a land surface similar to that modelled with the irrigated offline ISBA simulations. By entering values for Va,2, T and VPD either taken from atmo_NOIRR or atmo_IRR_FC, the overestimation due to the lack of atmospheric feedback in the input data can also be evaluated. The overestimation is found to be similar with the FAO-56 formula as with the offline ISBA simulations, i.e. between 20 % and 24 %. The average overestimation for all cases including irrigation (i.e. Irrigated and FAO-56) is 25 %.