Quantification of uncertainty in reference evapotranspiration climate change signals in Belgium

Evapotranspiration (ET) is a main flux term in the water cycle and an important process in the climate system, thereby playing a key role in water and energy balance. It is also vital for climate change impact studies, drought prediction and monitoring, agricultural water requirement planning and effective management of water resources. Specifically for hydrology, reference ET (ET_o) is a necessary component for computing actual ET for a watershed as a function of soil moisture deficit and a key input parameter for hydrological water-balance models (Bergström et al. 2001; Obeysekera 2013; Tabari & Hosseinzadeh Talaee 2014; Meng et al. 2016). ET_o is, moreover, used to assess the hydrological impact of climate change at catchment scales (Taye et al. 2011; Ntegeka et al. 2014; Vansteenkiste et al. 2014; Rudd & Kay 2016).

Climate change is one of the most critical global problems of our time (IPCC 2007), which may influence watershed hydrology and water availability by changing the patterns of precipitation and ET (King et al. 2015). Future changes in ET rate together with changes in precipitation patterns will affect runoff and water balance and consequently water infrastructure design (Prudhomme & Williamson 2013; Mohor et al. 2015; Koedyk & Kingston 2016).

There are numerous methods to estimate ET_o based on meteorological data ranging from simple temperature (e.g., Hargreaves–Samani: Hargreaves & Samani 1985) or radiation (e.g., Jensen–Haise: Jensen & Haise 1963) based methods to complex Penman family methods (e.g., Penman: Penman 1948; Kimberly–Penman: Wright 1982). Among them, the Penman–Monteith FAO 56 (PMF-56) method was strongly recommended by the United Nations Food and Agriculture Organizations (FAO) and the American Society of Civil Engineers (ASCE) as a standard method for ET_o estimation (Allen et al. 1998; ASCE-EWRI 2005), because the PMF-56 method incorporates most of the meteorological variables controlling the ET process. Nevertheless, to simplify the process of ET_o estimation due to limited time and/or budget and in some cases because of unavailability of the full meteorological data required for the standard PMF-56 method, simple, empirical equations have been used in many climate change studies for this purpose (e.g., Immerzeel et al. 2012; Bastola 2013; Lu et al. 2013; Capell et al. 2013; Kopytkovskiy et al. 2015). The simple equations relate ET_o to an easily measured process variable such as temperature and do not consider the effect of ‘advective’ variables (i.e., wind speed and vapor pressure) (Donohue et al. 2010). However, ET_o is primarily a function of four key weather variables of radiation, wind speed, humidity (or vapor pressure), air temperature and these variables must be considered for a better understanding of ET_o changes under climate change conditions (McVicar et al. 2012). The ET_o changes projected by simple approaches may differ substantially from those by the standard method that may add uncertainty to derived climate change signals (CCS) and future water balance projections (Kingston et al. 2009; Bae et al. 2011; McAfee 2013; Thompson et al. 2014; Wang et al. 2015). Therefore, the existence of potential systematic bias or uncertainty in the derivation of ET_o CCS by using simple ET_o methods needs to be considered. The uncertainty in ET_o CCS by simple methods is, however, largely unknown. This research gap is addressed in this paper. More specifically, the bias in ET_o CCS obtained from seven simple methods (Blaney–Criddle, Hargreaves–Samani, Schendel, Makkink, Turc, Jensen–Haise, Tabari) compared with those from the PMF-56 method as a benchmark is investigated under different time resolutions, i.e., seasonal, monthly and daily.

The general circulation model-Coupled Model Intercomparison Project Phase 5 (GCM-CMIP5) ensemble considered for this study consists of 12 GCMs (listed in Table S1 with their respective resolution; Table S1 is available with the online version of this paper). All the meteorological data needed for ET_o estimation by the PMF-56 method (which include those needed for seven simple methods) were obtained from 264 CMIP5 GCM runs (44 runs for each of six meteorological variables including maximum, minimum, and mean temperature, radiation, wind speed, and humidity). In fact, all the GCMs providing the complete set of meteorological inputs for ET_o estimation were selected. Although some authors recommend 50-year periods (Bonell & Bruijnzeel 2005), in this study the period 1961–1990 was applied as the control period. This period is recommended by WMO (2007) and commonly applied in climate change studies. The period 2071–2100 was considered as the scenario period. Four 21st century scenarios for future greenhouse gas concentrations including RCP2.6, RCP4.5, RCP6.0, and RCP8.5 were considered, where RCP8.5 represents the highest concentrations and RCP2.6 corresponds to the lowest concentrations (Moss et al. 2010). The analyses were done for the GCM grid cell covering central Belgium.

After extracting all the meteorological data from the GCMs, ET_o is calculated by different methods, that are briefly explained in the next section. Daily ET_o values are averaged to obtain monthly ET_o. Afterwards, CCS are derived for both daily and monthly ET_o as the difference between the values for the scenario period (2071–2100) and those for the control period (1961–1990). The changes in daily ET_o are shown by means of box-and-whisker plots for summer and winter seasons. The calculation of these results involves the following steps:

1. For each ET_o model, separate the ET_o results for summer (JJA: June, July, August) and winter (DJF: December, January, February) seasons.

2. Calculate CCS as the difference between the ET_o values for the scenario and control periods of each GCM out of the total 12 GCMs:

   

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3. Combine CCS of all GCMs.

4. Calculate climate change signals in percent by dividing the combined signals obtained from step 3 over the median of all GCMs' ET_o values for the control period ⁠:

   

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5. Compute 5%, 25%, 50%, 75%, and 95% percentiles of the signals (%) and show the results in a box-and-whisker plot.

High, mean, and low climate scenarios for monthly or daily ET_o change are later defined as 95%, 50%, and 5% quantiles of the relative changes. For the monthly ET_o, the changes are considered as such; for the daily ET_o, the changes are considered as changes in the quantiles (percentiles). As the changes in high ET rates are of vital importance for drought monitoring and agricultural water planning and management, the changes in high daily ET_o quantiles (percentiles) are also investigated.

In this study, the ET_o CCS derived from the PMF-56 method are compared with the ones from three temperature-based (i.e., Blaney–Criddle, Hargreaves–Samani and Schendel) and four radiation-based (i.e., Makkink, Turc, Jensen–Haise, and Tabari) methods.

Bias in the mean scenario of seasonal ET_o calculated based on the simple ET_o methods is presented in Table 1. As the results indicate, the performance of the simple methods changes seasonally. The Hargreaves–Samani, Makkink, and Tabari methods underestimate the mean scenario and the rest of the methods overestimate it. In winter, the best performance in estimation of the mean scenario for seasonal ET_o is produced by the Hargreaves–Samani, Tabari and Jensen–Haise methods, while the Makkink and Tabari methods perform the best in spring. The mean scenario for summer ET_o is underestimated by most of the simple methods, among which Turc and Schendel show the smallest biases. For autumn, the Tabari and Makkink methods more closely reproduce the PMF-56-driven scenario. Overall, among all the simple methods, Schendel has the worst performance in estimation of monthly and seasonal ET_o changes.

The results obtained indicate that the ET_o change signals projected by the simple methods broadly follow the pattern of those by the PMF-56 method. However, the magnitude of the changes differs substantially between the simple and standard method. The main reason for such difference is the inclusion of more meteorological variables controlling the ET process in the PMF-56 method. Moreover, simple ET_o approaches with the same meteorological inputs present different CCS. This difference stems from the difference in empirical formulation for each approach and the difference in climatic regions for which they were originally developed. Let us consider the drawback of the Hargreaves–Samani method as the most widely used simple approach in hydrological impact studies of climate change. First of all, the Hargreaves–Samani method uses extraterrestrial radiation rather than solar radiation, implying the use of maximum possible radiation and neglecting atmospheric transmissivity. The existence of high moisture content in the atmosphere in humid regions influences transmissivity or sky clearness and leads to an increase of the attenuation of solar radiation at the surface (Fontenot 2004). The other important variable in humid regions is atmospheric moisture, which is not considered in the Hargreaves–Samani method. Atmospheric moisture (directly correlated with vapor pressure) has an indirect relationship with ET, and in fact, ET decreases as atmospheric moisture increases (McKenney & Rosenberg 1993; Tabari 2010; Moratiel et al. 2010). These two important factors result in bias in the estimates of the Hargreaves–Samani method. The calibration of the method to local conditions may decrease this bias (Tabari & Hosseinzadeh Talaee 2011).

The findings show that choosing an alternative method to the PMF-56 method with less data demand is difficult. The performance of the simple methods varies remarkably by time scale and season. Taking the mean scenario into account, the Hargreaves–Samani, Makkink, Turc and Tabari methods are the best choices for seasonal and monthly ET_o climate change studies in winter, spring, summer, and autumn, respectively, while the Turc, Jensen–Haise and Hargreaves–Samani methods perform best for investigation of the changes in high ET_o percentiles. This suggests using different simple methods for different time scales and seasons in the absence of full meteorological data for the PMF-56 method application.

In order to investigate the importance of the uncertainty associated with ET_o methods, it is compared with GCM uncertainty which is considered as the main source of uncertainty in climate change studies (Wilby & Harris 2006; Kay et al. 2009; Chen et al. 2011; Exbrayat et al. 2014) and also that of future greenhouse gas scenarios (RCP). For the monthly ET_o change and also taking the full range of daily ET_o change into consideration, the uncertainty in GCMs is larger than that in the ET_o methods and RCPs (Table 2). For both mentioned cases, the ET_o uncertainty is of comparable magnitude to the GCM uncertainty. As for the changes in high daily ET_o percentiles, the uncertainty related to the ET_o methods is the dominant source of uncertainty for both summer and winter seasons, while RCP has the lowest contribution to the total uncertainty in ET_o changes. Generally, the uncertainty analysis shows that the uncertainty in ET_o methods is noticeable for all the cases considered. This shows the importance of addressing the uncertainty associated with ET_o methods next to that in GCMs and future greenhouse gas scenarios as is traditionally done.

In this study, the difference between the ET_o CCS derived from the standard PMF-56 method and those from seven simple methods (Blaney–Criddle, Hargreaves–Samani, Schendel, Makkink, Turc, Jensen–Haise, Tabari) was investigated. The meteorological data required for ET_o estimation by the methods were obtained from 12 CMIP5 GCMs for control (1961–1990) and scenario (2071–2100) periods. The results show that the standard and the simple methods generally agree on ET_o increase for all time scales, but disagree on the magnitude of the increase. Biases of over 100% are found for CCS extracted from some simple methods such as Turc and Schendel.

A comparison between the uncertainties related to ET_o methods and GCMs shows that the uncertainty associated with ET_o methods is of comparable magnitude to GCM uncertainty as the main source of uncertainty, suggesting that the uncertainty in the choice of ET_o methods must not be neglected in such studies. Use of further advanced methods for ET_o estimation, which is a function of time scale and season (as the results of this study show), may reduce the uncertainty associated with ET_o methods. Comparing the ET_o uncertainty with the other sources of uncertainty, such as GCM boundary conditions, was impossible in this study because of the limited number of GCM runs providing all meteorological inputs for the ET_o methods. This type of comparison can be made for precipitation as another important input for hydrological modeling in future studies. The uncertainty related to the choice of a downscaling method was not addressed in this study. Thus, further work is needed to assess the degree to which the choice of the statistical method to transfer the climate change signal to the hydrological model inputs, i.e., the downscaling method, contributes to the total uncertainty. Moreover, the effect of the different sources of uncertainties affiliated with precipitation and ET_o may be explored for hydrological impact projections.

To conclude, considering the large bias of the simple ET_o methods, a fully physically based formulation of ET_o like the PMF-56 method is recommended for projecting ET CCS. This, moreover, requires that the climate modeling centers produce and provide model outputs for all meteorological variables governing the evaporative process. In the case of data unavailability, the simple methods must be used with caution. The bias in the results of the simple methods depends on the time scale and season, as is shown in this study for central Belgium. This bias obviously may differ for other regions of the world.

The authors acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, and the climate modeling centers involved for the CMIP5 model outputs.