MODELING EVAPOTRANSPIRATION DURING INTER-STORM PERIODS IN A MEDITERRANEAN CLIMATE AREA

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1 Proceedings of the 13 th International Conference on Environmental Science and Technology Athens, Greece, 5-7 September 2013 MODELING EVAPOTRANSPIRATION DURING INTER-STORM PERIODS IN A MEDITERRANEAN CLIMATE AREA E.S. KHAERTDINOVA 1, and A. LONGOBARDI 2 1 Department of Production Safety and Industrial Ecology, Ufa State Aviation Technical University, Ufa , Russian Federation, 2 Department of Civil Engineering, University of Salerno, Fisciano (SA) 84084, Italy alongobardi@unisa.it ABSTRACT Evapotranspiration represents an important component of the water fluxes of our hydrosphere and atmosphere and is a widely studied variable throughout the world. Scientists consider evapotranspiration as an important process to be modelled for the practical purpose of water resource management. The make distinction between potential and actual evapotranspiration. Among the two, the actual rate represent the most interesting evapotranspiration process, because close to the real conditions, but it is also the mostly difficult process to be modelled. Different methods can be proposed for actual evapotranspiration assessment. If soil moisture data are available, it is possible to apply the soil water budget method, where evapotranspiration volume loss, during a given period of time, can be estimated as the difference in the water content stored into the soil. Another well-known methodology for actual evapotranspiration assessment, consist in the investigation of the relation existing between potential and actual rates and a large number of models have been proposed in the past literature for potential evapotranspiration rates estimation. In the following, soil moisture experimental data, recorded in a field site located in Southern Italy, are used to study the actual evapotranspiration dynamic during inter-storm period, and to relate it to the soil moisture dynamic. Keywords: inter-storm period, evapotranspiration actual and potential, soil moisture, air temperature, water balance model, Penman-Monteith and Priestly-Taylor models 1. INTRODUCTION Evapotranspiration (ET) is a central component of the global hydrological cycle (Fisher et al., 2009; Hasler and Avissar, 2006; Jimenez et al., 2011; Jung et al., 2010) and the accurate estimation of ET is very important for hydrological issues such as streams and lakes water balance assessment and management. Evapotranspiration is the sum of volume of water used by vegetation, evaporated from the soil and intercepted precipitation. The evaporation plus transpiration from a vegetated surface with unlimited water supply is known as potential evapotranspiration and it constitutes the maximum possible rate due to the prevailing meteorological conditions and assuming no control on water supply. Actual evapotranspiration is instead the quantity of water that is actually removed from a surface due to the processes of evaporation and transpiration. Scientists consider these two types of evapotranspiration for the practical purpose of water resource management. But among the two, the actual rate represent the most interesting evapotranspiration process, because close to the real conditions, and it is also the mostly difficult process to be modelled. Different methods can be proposed for actual evapotranspiration assessment (Wilson et al., 2001). If soil moisture data are available, it is possible to apply the soil water budget method, where evapotranspiration volume loss,

2 during a given period of time, can be estimated as the difference in the water content stored into the soil. Another well-known methodology for actual evapotranspiration assessment, consist in the investigation of the relation existing between potential and actual rates. A large number of models have been proposed in the past literature for potential evapotranspiration rates. The model that has been shown to have the higher reliability and accuracy in simulating the evapotranspiration dynamic is the Penman-Monteith (Penman, 1948; Monteith, 1965) able to take into account not only the energy forcing surface, but also the phenomena of crop resistance and aerodynamic features. By contrast, as a drawback, such a formulation requires a rather time consuming database of variable to be monitored for a particular field, besides the simple climate variables. The widespread use and the rather high prediction reliability have made this model as a reference approach in comparative studies (Rahimikhoob et al. 2012). The Priestley-Taylor model (Priestley and Taylor, 1972), which represent a simplification of the Penman-Monteith model, removing the aerodynamic resistance component, is a further well-known and widely used approach to assess maximum crop evapotranspiration fluxes. In the following, soil moisture experimental data, recorded in a field site located in Southern Italy, are used to study the actual evapotranspiration dynamic during inter-storm period, and to relate it to the soil moisture dynamic. 2. EXPERIMENTAL DATA ANALYSIS The experimental plot, a 450 m 2 (15 30 m) filed equipped with a meteorological station and six multi-level soil moisture measurements probes, is located in Southern Italy, within the University of Salerno s campus. The vegetation consists of perennial lawn grass. Grain size distribution of collected samples shows a layered soil profile: a first layer ranging from 0 to 20 cm classified as gravel with silt and clay, a second layer ranging from 20 to 60 cm classified as clay with silt sand and a third layer ranging from 60 to 80 cm classified as clayey silt with sand and gravel. Soil moisture time series, at the hourly scale, are available from the period October 2004 to December More details about the experimental plot can be found in Longobardi et al. 2006; Longobardi, 2008; Khaertdinova and Longobardi, In order to investigate the relation between soil moisture and evapotranspiration at the filed site, a number of about 30 inter-storm events have been selected. The reason for excluding rainy days from the current analysis, lies in the fact that movements of soil water within the soil profile consequent to the rainfall occurrences, can confounds estimates of soil water extraction by the soil water budget method in the following applied (Wilson et al., 2001). For each event, hourly soil moisture time series have been aggregated at the daily scale. A minimum number of five days has been herein considered. a) b) Figure 1. Observed inter-storm soil moisture dynamic, at 10 and 30 cm, for (a) dry season; (b) wet season.

3 Fig. 1 illustrates, as an example, the temporal dynamic for both a dry and wet seasons inter-storm events. Overall, as showed in the same picture, inter-storm events can be empirically described by an extremely simple negative exponential relation, where the exponential parameter α, describing the rate of soil moisture depletion, has been demonstrated to be dependent both on the seasonal and on the event scale. The rate of depletion is in fact larger during the hot growing season and for larger initial soil water content volumes. The same process also shows a dependence on the soil profile depth at which observations have been recorder, with the surface layer showing a faster decrease in soil moisture content compared to the deeper layers. The Southern Italy climate is indeed characterized by a hot and dry season in summer and a mild temperature associated to annual rainfall in winter. During summer, the simultaneous occurrences of high temperatures and small precipitation causes then high evapotranspiration rates. 3. MODELING ACTUAL EVAPOTRANSPIRATION FROM SOIL MOISTURE MEASUREMENTS During inter-storm period, that is a period of time between two successive rainfall events, the rainfall infiltration rate is absent, and the soil moisture variation over time is only driven by the rate of losses, mainly corresponding to the evapotranspiration. Water balance equation, for the inter-storm period in its simplified form, was used to calculate actual ET volume (expressed in mm) on the depth of 10 cm and 30 cm using recorded soil moisture data: ET ( 0 n) z (1) where 0 (%) is soil moisture content at the beginning of the inter-storm period, n (%) is the soil moisture content at the end of the inter-storm period and z (mm) is depth of soil layer where measurement have been recorded. In order to identify an empirical relation to be applied at the experimental site for actual evapotranspiration volume prediction, an explorative analysis has been undertaken, where the soil water content has been related to ET volume estimated from equation (1). Figure 2 illustrate, for the 10 and 30 cm, the relation, at the event scale, between ET volume and initial soil water content 0. The relationship between ET and 0 depicted in Figure 2, even though not extremely clear, indicate that there is a tendency between the two mentioned variables, with increasing ET for increasing 0: the large soil water availability allows indeed larger evapotranspiration losses as it would have been expected from a conceptual point of view. a) b) Figure 2. Relation between ET volume and initial soil moisture content 0: a) 10 cm depth; b) 30 cm depth.

4 This consideration appear even more stronger if the ratio k=et/pet between the actual to potential evapotranspiration is plotted against the initial soil water content θ 0. The k dimensionless coefficient is more strongly related to the θ 0, as indicated in Figure 3, both for the surface and the deep layers: small ET volume estimated for large θ 0, above the 25%, responsible for the large scattering in Figure 2, are characterized by PET volume of the same order of magnitude and then result in maximum k indices. The fact that k is lower than 1, at least for the 10 cm, for each of the selected events, would indicate that, for each event, PET is always larger that ET and this is an indication of the condition that actual ET is limited by soil water availability for the experimental site. a) b) Figure 3. Relation between K and θ 0: a) for 10 cm; b) for 30 cm. On a practical base, the feasibility for an empirical relation between actual evaporation and soil water content seems to be evident, but the calibration of such a relation for a particular site would require a soil water monitoring campaign lasting, at least, for one hydrological year, in order to capture the full range of soil water content availability. It is known that soil moisture measurements are not as widely available as other climate variable, such as the air temperature, which could be potentially related to actual evapotranspiration rates occurrences. 4. MODELING ACTUAL EVAPOTRANSPIRATION FROM AIR TEMPEARTURE MEASUREMENTS Similarly to what has been commented in the previous paragraph, the relation between ET volume and average air temperature, during the particular considered inter-storm event, is herein investigated. Figure 4 illustrate, for the 10 and 30 cm, the relation, at the event scale, between ET volume and average air temperature T C. No relation between ET and T appear to be existent, for both the surface and, with stronger reason, for the deep layer, as depicted in Figure 4. This condition could be an indication of the fact that given the particular climate condition of the experimental site, major evapotranspiration control is exerted by the soil water availability rather than by the climate forcing air evaporation, as already stressed in virtue of the results about the dimensionless index k, given in Figure 2.

5 a) b) Figure 4. Relation between ET volume and average air temperature T ( C): a) 10 cm depth; b) 30 cm depth. As well as done for the soil water content availability, the feasibility for an empirical relation between actual evaporation and air temperature seems not to be evident on a direct measurements base. Air temperature can be however used in order to calculate potential evapotranspiration volumes at the daily scale, which can be compared to actual volumes, with the aim to identify the potential relation existing between potential and actual evapotranspiration rates at the particular experimental site. а) b) Figure 5. Relation between ET 0 and θ 0: a) Penman-Monteith model; b) Priestly-Taylor model A large number of methods have been developed for assessing potential ET from meteorological data. In case of reduced set of observed variables, it is possible to apply a number of formulas in a simplified context, proposed in literature. In a previous study concerning the experimental studied site the Penman Monteith and Priestley-Taylor models have been used to calculate potential ET, which comparison with observed value, measured with a micrometeorological instrumentation for a short period of time, appear rather satisfactory. (Longobardi and Villani, 2013). To model potential evapotranspiration (ET 0) for the analyzed inter-storm periods (October 2004 to December 2007), the Penman-Monteith model (equation (2)), which considers the evapotranspiration rate as a combination of mass and surface energy balance and introduces the concepts of canopy and aerodynamic resistances, and the Priestly-Taylor model (equation (3)), which proposes a simplification of the Penman-Monteith model, removing the aerodynamic resistance component, were applied: (2)

6 (3) where Rn is the net solar radiation (MJ m-2 d-1), G is the soil heat flux (MJ m-2 d-1), T is the average daily air temperature ( C), u 2 is the wind speed at two meters above the soil surface (m/s), es the saturation vapor pressure (Pa), ea the actual vapor pressure (Pa), Δ is the slope of the saturation-to-vapor-pressure curve (Pa C-1), and γ the psychrometric constant (kpa C-1). Figure 6. Relation between ET 0 and T: a) Penman-Monteith model; b) Priestly-Taylor model In order to identify an empirical relation to be applied at the experimental site for actual evapotranspiration volume prediction, an explorative analysis has been undertaken, where the soil water content and the air temperature have been related to ET 0 volume estimated from equations (2) and (3). Figure 5 illustrates, for the Penman-Monteith model (PM) and for the Priestly-Taylor model (PT), the relation, at the event scale, between ET 0 volume and initial soil water content 0. Figure 6 illustrates instead, for the Penman- Monteith model (PM) and for the Priestly-Taylor model (PT), the relation, at the event scale, between ET 0 volume and average air temperature T. Given the fact that the modeling approaches used are based on temperature data as model input, the dependence between modeled ET 0 and T is rather evident whereas the dependence on the initial soil water content does not appear really consistent. Subsequently, the correlation between actual evapotranspiration volume and potential ones is investigated. As an example, Figure 7 shows the dependence when the Penman- Monteith model is applied for ET 0 assessment. According to the literature analysis, potential volumes overestimates actual volumes since they are associated to the hypothesis of maximum water content availability. The rate of overestimation obviously occur for the large value of ET 0: these would indeed correspond to the summer period when potential rates are predicted very high because of the high air temperature but actual rates are strongly limited by the limited soil water availability caused by rainy deficiency during the summer period.

7 Figure 7. Relation between actual ET and potential ET 0 (Penman-Monteith model). 5. CONCLUSIONS The paper has presented an analysis aimed at understanding the evapotranspiration dynamic during inter-storm period for a particular experimental plot, located in Southern Italy. When soil moisture data are available, then it has been showed that there is the feasibility to calibrate an empirical model which relate the initial soil water content, for a particular inter-storm event, to the actual evapotranspiration loss volume occurring during that inter-storm event. But soil moisture data are not widely available, whereas more climatic variables could be used as predictor of actual evapotranspiration rates. Among these, the air temperature has been presented as potentially useful to predict actual evapotranspiration. Potential ET 0 volumes have been modeled using the Penman- Monteith model and Priestly-Taylor model for each of the analyzed inter-storm period. Et 0 event volumes have then been compared to event actual volumes and an empirical relation has been calibrated among the two. Prediction accuracy, when air temperature is used as a predictor, is not as good as in the case of soil moisture data availability, but provide quick and useful result for modeling purposes. An explanation for such findings can be found in the fact that given the experimental site climate conditions, sol water content availability is the major control on evapotranspiration losses process. REFERENCES 1. Penman H.L. (1948) Natural evapotranspiration from open water, baresoil, and grass, Proc. R. Soc. Lond. A, 193, Monteith J.L. (1965). Evaporation and environment. In Fogg editor. The state and movement of water in living organism, Soc. Exp. Biol. Symp, 19, Rahimikhoob A., Behbahani M.R. and Fakheri J. (2012) An Evaluation of Four Reference Evapotranspiration Models in a Subtropical Climate, Water Resources Management, 26, Priestly C.H.B. and Taylor R.J. (1972) On the assessment of surface heat flux and evaporation using large scale parameters. Monthly Weather Review, 100, Longobardi A., Villani P., Foresta V. and Sorbino G. (2006) An experimental plot for hydrological processes modeling. In Hamza M.H. editor. IASTED International Conference on Applied Simulation and Modeling (ASM2006); Longobardi A. (2008) Observing soil moisture temporal variability under fluctuating climatic conditions, Hydrology and Earth System Sciences Discussion, 5,

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