Advances in Meteorology

Volume 2018, Article ID 9792609, 13 pages

https://doi.org/10.1155/2018/9792609

## A Semiempirical Method to Estimate Actual Evapotranspiration in Mediterranean Environments

^{1}Institute of Biometeorology, CNR, Sesto Fiorentino 50019, Italy^{2}LaMMA Consortium, Sesto Fiorentino 50019, Italy

Correspondence should be addressed to Fabio Maselli; ti.rnc.temibi@illesam.f

Received 26 July 2018; Accepted 29 October 2018; Published 29 November 2018

Academic Editor: Harry D. Kambezidis

Copyright © 2018 Marta Chiesi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Actual evapotranspiration (ET_{A}) is a major term of site water balance whose knowledge is essential for numerous purposes. The classical ET_{A} estimation approach based on the use of multitemporal crop coefficients (Kc) cannot be applied in water-limited environments without proper correction. Such correction can be theoretically obtained by means of soil water content (SWC) measurements, which, however, are affected by several drawbacks, due to both their technical and operational characteristics. The current paper proposes a method to normalize annual SWC datasets and integrate them in an ET_{A} estimation procedure suitable for monitoring both agricultural and natural Mediterranean ecosystems. Differently from previous approaches, the SWC normalization is obtained using data-specific information, which renders the new method mostly insensitive to the mentioned problems. The method is first described and then applied in three case studies representative of different Mediterranean ecosystems (i.e., grassland, coniferous, and deciduous forests). The results are evaluated versus latent heat measurements taken by eddy covariance flux towers. Satisfactory accuracy is obtained in all three case studies, with advantages and limitations which are discussed in the final concluding sections.

#### 1. Introduction

Arid and semiarid areas are increasingly affected by water scarcity due to the growing request of this resource for several conflicting uses. This is particularly the case for Mediterranean environments, which are characterized by prolonged summer aridity and are very vulnerable to ongoing climatic change [1]. Consequently, numerous initiatives have been promoted for achieving more efficient and sustainable uses of water resources in Mediterranean countries [2].

Actual evapotranspiration (ET_{A}) is one of the main terms of the water cycle whose monitoring is important for both scientists and practitioners working in different fields, such as meteorologists, agronomists, ecologists, and landscape planners. Numerous methodologies have therefore been developed to measure ET_{A}, which differ for the basic principles utilized (i.e., energy balance or water balance methods), for the spatial and temporal scales of investigation, and for what is being effectively measured (evapotranspiration itself or one of its components, i.e., evaporation and transpiration) [3].

Among energy balance methods, the eddy covariance technique is widely applied to measure the sensible heat flux over the canopy of vegetation. This technique provides measurements related to the so-called footprint area, whose size and shape can vary during time following wind directions [3]. Additionally, eddy covariance measurements can provide only point observations and are very expensive to collect over long-time periods.

In contrast, water balance methods can be easily applied at different spatial and temporal scales based on a reduced amount of input data. Some of these methods are based on the integration of meteorological data and soil water measurements taken by using a lysimeter [4]. When this instrument is not available, a common alternative is given by probes measuring soil water content (SWC, in cm^{3}·cm^{−3}) [5, 6]. These methods, however, are particularly susceptible to possible problems arising from the poor representativeness of SWC data, which are often collected only for a single soil layer and can hardly describe the conditions of the whole soil profile [7]. Moreover, the collected SWC datasets are often affected by troubles over medium-long time periods due to maintenance problems and to the high variability of measurement conditions which affects soil sensors [6]. Consequently, SWC measurements are indicative of relative SWC variations in time but can hardly be utilized for the quantitative estimation of the soil water balance and ET_{A} [8].

An operational alternative is provided by the consolidated Kc approach [9], which corrects potential evapotranspiration (ET_{0}) by means of multitemporal plant-specific coefficients estimated by different techniques [10]. The original Kc approach, however, assumes that the observed ecosystems are not affected by water limitation and is therefore ineffective for nonirrigated crops or natural vegetation types. A solution to this problem is provided by the consideration of an additional water stress coefficient obtained using SWC as a surrogate of water shortage information [9]. This approach still has to face the mentioned drawbacks of SWC observations, which can seriously deteriorate the quality of the utilized water stress indicators.

The current work addresses this issue by developing and testing a semiempirical method which combines environmental, meteorological, and SWC data for the operational estimation of ET_{A} in water-limited Mediterranean environments. The next section provides a brief description of the classic Kc approach, followed by the introduction of the proposed method. This method is then applied in three case studies representative of different Mediterranean biome types and environmental conditions. A discussion of the strengths and weaknesses of the methodology is then presented together with the main conclusions of the investigation.

**2. Proposed ET**_{A} Modelling Strategy

_{A}Modelling Strategy

The classical method to estimate ET_{A} proposed by FAO is based on the use of time-varying crop coefficients (Kc), defined as the ratio of the ET_{A} observed for the crop studied over ET_{0} [9]. According to this approach, the ET_{A} on day *i* is estimated as follows:where Kc_{i} is the crop coefficient on the same day, which is strictly dependent on the characteristics of the crops/plants considered and is usually determined by semiempirical methods [9]. In general, the annual plant cycle is divided into five distinct periods showing different crop coefficients: (i) Kc_{ini}, which corresponds to a minimum ET_{A} rate of the crop with respect to a reference coverage (well-watered reference grass); (ii) Kc_{growth}, which is typical during the phase from 10% ground cover to an effective full cover and is obtained by means of a linear ramp function from the predetermined Kc_{ini} to the next Kc_{mid}; (iii) Kc_{mid}, which represents the maximum ET_{A} rate during the annual plant cycle, from full development to maturity; (iv) Kc_{late}, corresponding to the reduction of plant efficiency during the late season, from maturity to harvest or leaf fall. Similarly to Kc_{growth}, Kc_{late} is computed as a linear function from Kc_{mid} to Kc_{end}; and (v) Kc_{end}, which is detected at the moment of plant harvest or at the end of the season.

This original Kc approach does not consider water limitation and requires the basic assumption that the observed vegetation is growing under unstressed water conditions [9]. The approach is therefore suitable for simulating ET_{A} in ecosystems where water stress is negligible (i.e., in humid or irrigated areas) but produces substantial ET_{A} overestimation in water-limited environments [11]. A solution to this problem is provided by using SWC measurements to correct the ET_{A} estimated by the classical Kc approach in case of water limitation [12]. SWC, in fact, is a direct indicator of the water which is available for both soil evaporation and plant transpiration. Equation (1) is consequently modified into the following equation:where Ks_{i} is the water stress coefficient on day *i*, derivable from SWC data. The relationships between SWC and transpiration, however, are complex and variable depending on a number of environmental factors (mainly soil and vegetation features). A good review of this subject is provided by Verhoef and Egea [13], who report several different functions relating relative transpiration to the fraction of transpirable soil water (FTSW). Similarly, soil evaporation is usually considered to depend on FTSW [13].

An additional problem is related to the numerous sources of uncertainty which affect SWC measurements. These measurements, in fact, can provide only local (point) observations, usually referred to a small soil sample (few cubic centimeters) around the probe [6]. Thus, vertical and horizontal SWC variations out of this area, which are considerable in most real cases, cannot be detected. In particular, SWC measurements are usually taken at limited soil depth (20–50 cm) and cannot be representative of all conditions affecting plant roots, i.e., the so-called “rooting zone,” that can be much deeper. SWC probes may also suffer from lack of representativeness for the presence of air gaps in the soil, from poor calibration, and/or from temporal drifting, which further complicate the utilization of the measured data [5, 6].

The semiempirical method currently put forward circumvents these issues by elaborating the available SWC measurements based on data-specific information. In particular, the method utilizes relative SWC (RSWC) to correct the ET_{A} estimated by the original Kc approach assuming a linear relationship between the two variables. This assumption is theoretically justified by the mentioned complexity and variability of the actual relationships between ET_{A} and RSWC [13] and is practically necessary to minimize the number of parameters to be identified. As is schematized in Figure 1, in fact, a linear equation relating relative ET_{A} (RET_{A}) to SWC can be defined identifying the two extreme points, i.e., the SWC corresponding to full and null evapotranspiration, which can be assumed to correspond to field capacity (SWC_{fc}) and permanent wilting point (SWC_{wp}), respectively [8].