Assessment of pan coefficient models for the estimation of the reference evapotranspiration in a Mediterranean environment in Turkey

Study area

In the present study, the Adana weather station (latitude = 37°00′14″N; longitude = 35°20′39′E) located in central Adana operated by the Turkish State Meteorological Service (TSMS) is used to assess pan coefficient models. Adana plain is Turkey’s most extensive and fertile delta plain (Fig. 1). It consists of two parts called Çukurova and Upper Plain (Kafalı Yılmaz, 2019). Adana has a hot-summer Mediterranean climate. The study area is on flat terrain at an altitude of 24 m above sea level. According to Köppen–Geiger classification, Adana is Csa (warm temperate, summer dry, hot summer) (Öztürk, Çetinkaya & Aydın, 2017). According to the long-term measurement period (1929–2020), the rain in Adana falls mainly in the winter. The average annual rainfall is 668.1 mm, of which about 50% of rainfall occurs in December, January, and February, the three winter months. The months with the least precipitation are July and August, with an average of 10.2 and 9.6 mm, respectively. June and August are the hottest months, with a mean daily temperature of 28.2 and 28.7 °C, whereas January and February are the coldest months, with a mean daily temperature of 9.5 and 10.5 °C, respectively (Turkish State Meteorological Service, 2021). According to the long-term measurement period (1990-2019), the daily mean relative humidity is 65.8% in winter months while it is 68.9% in summer months, and its annual average is 66.0%. In the same measurement period, the daily mean wind speed is 1.33 in the winter months, whereas it is 1.40 in the summer months, and its annual average is 1.31 m s⁻¹ (Turkish State Meteorological Service, 2020).

Models and approaches

Eight pan coefficients (K_pan) models derived from some weather data were tested and summarized below in Table 1. Long-term daily climatic parameters from 1998 to 2019 were used for this study.

FAO-56 PM method was used to test the accuracy of the ETo estimated by K_pan models because FAO recommended it for different climatic conditions (Allen et al., 1998). (1)${\displaystyle \mathrm{ETo}=\frac{0.408\times \Delta \times \left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+\gamma \times \frac{900}{\mathrm{T}+273}\times {\mathrm{U}}_2\times \left({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}}\right)}{\Delta +\gamma \times \left(1+0.34\times {\mathrm{U}}_2\right)}}$

where ETo = reference evapotranspiration (mm d⁻¹); Δ = slope of vapor pressure curve (kPa.° C⁻¹); R_n = mean daily net radiation (MJ m⁻² d⁻¹); G = mean daily soil heat flux density (MJ m⁻² d⁻¹); γ = psychrometric constant (kPa K⁻¹); T = mean daily air temperature at 2 m height (°C); U₂ = mean daily wind speed at 2 m height (m s⁻¹); e_s = saturation vapor pressure (kPa); and e_a = actual vapor pressure (kPa); (e_s – e_a) = saturation vapor pressure deficit (kPa) (Allen et al., 1998).

In this study, the ETo software (IAM_ETo) developed by Steduto & Snyder (1998) was used for determining the FAO-56 PM reference evapotranspiration. All of the data processing and calculations were performed in Microsoft Excel 2016.

Based on the FAO-24 Pan equation developed by Doorenbos & Pruitt (1977), pan evaporation data were converted to ETo using Eq. (2). (2)${\displaystyle ETo=K_{\mathrm{pan}}\times E_{\mathrm{pan}}}$

where K_pan = pan coefficient; E_pan = pan evaporation (mm d⁻¹).

The ‘observed’ Class A pan coefficients were calculated by dividing FAO-56 PM ETo values by E_pan values (Eq. (3)). (3)${\displaystyle K_{pan-obs.}=\frac{ETo}{E_{pan}}.}$

Statistical analysis

A two-tail Z test was conducted to determine if the observed and models-estimated seasonal mean K_pan values differed significantly. Daily mean K_pan values observed and estimated during April-October in the years 1998–2019 were used in the Z-test. In addition, the five statistical parameters suggested by Karunanithi et al. (1994) and Jacovides & Kontoyiannis (1995) were used in the evaluation of the pan coefficient models in estimating ETo (Table 2). These five indices were calculated at the monthly and seasonal scales.

Estimation of pan coefficients

This study calculated daily and monthly mean K_pan values using eight K_pan models. The pan coefficients obtained using K_pan models and the FAO-56 PM equation are presented in Table 3. The pan coefficient values estimated using K_pan models showed a slight change during the season for each month, while those observed by FAO-56 PM showed variation among the months. It can be seen in Table 3 that K_pan values estimated by the Snyder model were higher than those of other models in all months during the season, while the Orang model gave lower pan coefficient values. The mean monthly pan coefficients during the season estimated by K_pan models ranged from 0.38 to 0.85, and those observed by FAO-56 PM ranged from 0.68 to 0.87. Allen & Pruitt (1991) and Babakos et al. (2020) reported that the range of pan coefficient values is nearly between 0.35 to 1.1 for various pan types and various local conditions of climates and surrounding environments.

As shown in Table 3, observed K_pan values were lower in dry months (July, August, September), whereas they were higher (April and May) in the rainy months. Similar results have been found in the studies performed in a Mediterranean environment by Aschonitis, Antonopoulos & Papamichail (2012) and in a humid tropical climate by Pradhan et al. (2013). Aschonitis, Antonopoulos & Papamichail (2012) assessed six K_pan models by two years of E_pan measurements using ASCE-PM as a reference in the Thessaloniki plain in Greece, which has a semi-arid Mediterranean environment. They likewise determined that observed K_pan values were higher in rainy months (April and May) and lower in dry months (June, July, August). The mean monthly K_pan values estimated by K_pan models ranged from 0.32 to 0.75, and those observed by ASCE-PM ranged from 0.67 to 0.76.

The pan coefficient depends on wind speed (U), relative humidity (RH), and upwind fetch distance.

As shown in Table 3, observed K_pan values were 0.87 and 0.80 in April and May, respectively, whereas they ranged from 0.68 to 0.73 from June to October. However, K_pan coefficients estimated by models indicated a slight change in all months because RH and U values changed slightly during the season. The Snyder model estimated close to observed K_pan values in April and May, whereas the Wahed & Snyder model estimated close to observed K_pan values in August. In contrast, the Modified Snyder, Cuenca, Allen & Pruitt, Pereira, and Raghuwanshi & Wallender models estimated K_pan values close to observed K_pan values in May.

According to Z-test, the results showed that mean seasonal pan coefficients estimated by all K_pan models during April-October in the years 1998–2019 differed significantly at a 1% significance level from those observed by FAO-56 PM (p < 0.01, n = 214). The results were given in Table S1.

Estimation of reference evapotranspiration

The daily Class A pan evaporation data and pan coefficients determined by K_pan models were used to estimate reference evapotranspiration (ETo). The ETo values estimated by eight K_pan models were tested against those calculated using the FAO-56 PM equation.

The performance of the K_pan models according to RMSE, MAE, and RE statistics for seasonal scale is shown in Figs. 2 and 3. It can be seen from the scatter plot that the performance of the K_pan models varied for the seasonal scale. None of the K_pan models could estimate the ETo satisfactorily, but the Wahed & Snyder model had better performance to estimate ETo for the seasonal scale than other models (RMSE = 0.550 mm d⁻¹; MAE = 0.425 mm d⁻¹; RE = 0.134). The Wahed & Snyder model tended to underestimate ETo values during the season. In contrast, the Snyder, Modified Snyder, Cuenca, Allen & Pruitt, Pereira, and Raghuwanshi & Wallender models often overestimated ETo values. The Orang K_pan model underestimated ETo values during the season. It can be seen in Fig. 3 the Orang model resulted in the highest relative error at the seasonal scale [RE (%) = 45.5] compared to other models. According to the results, the accuracy of the K_pan models was as follows ranking. Wahed & Snyder >Modified Snyder >Cuenca >Raghuwanshi & Wallender >Pereira >Allen & Pruitt >Snyder >Orang.

Similarly, Aschonitis, Antonopoulos & Papamichail (2012) reported that Snyder and Orang were the worst models to estimate ETo in a semi-arid Mediterranean environment in Thessaloniki in Greece. However, they found that the Cuenca model indicated the best adaptation to the ASCE PM equation compared to the other K_pan models. Grismer et al. (2002) concluded that among the six K_pan equations and FAO-24 table, the Allen and Pruitt K_pan model yielded better ETo estimations than other K_pan models in California conditions with a Mediterranean climate. Cobaner (2013) used three pan-based equations: the FAO-24 Pan (Doorenbos & Pruitt, 1977), the Snyder ETo (Snyder et al., 2005), and the Ghare ETo (Ghare, Porey & Ingle, 2006) in the Fresno and Bakersfield weather stations located in California, which has a Mediterranean climate. In his study, the daily Class A pan evaporation and reference evapotranspiration data are used as inputs to the wavelet regression (WR) models to estimate the ETo obtained using the FAO-56 PM equation. The performance of the WR models is compared with those of empirical models and their calibrated versions. His study selected the Allen & Pruitt K_pan model for the FAO-24 Pan equation because Grismer et al. (2002) determined it as the best K_pan model in California conditions. The WR model and the FAO-24 Pan equation yielded more accurate ETo estimation than those of the Snyder ETo and Ghare ETo equations. The WR model performed slightly better in predicting the ETo than the FAO-24 Pan equation. Trajkovic & Kolakovic (2010) evaluated the reliability of pan-based approaches (FAO-24 Pan, Snyder ETo, Ghare ETo) for estimating ETo, comparing them against daily lysimeter data from Policoro, Italy, which has a semi-arid Mediterranean climate. K_pan values obtained by radial basis function (RBF) were used in the study because Trajkovic & Kolakovic (2010) presented that the RBF network predicted K_pan values better than the K_pan equations of Frevert, Hill & Braaten (1983) and Snyder (1992). The results indicated that the Snyder equation estimated the ETo better than the FAO-24 Pan equation, although it does not require the relative humidity and wind speed data. Estimating the pan coefficients with the RGF model but not determining the most appropriate pan coefficient model for the region may have caused this result. In a study conducted by Gundekar, Khodke & Sarkar (2008) in semi-arid conditions in India, Pereira, Cuenca, and Orang K_pan models showed the worst performance to estimate ETo. However, the Snyder K_pan model showed the best performance to estimate ETo in the study. Sabziparvar et al. (2010) also reported that the Snyder K_pan model gave the best performance for the warm-arid climate of Iran. On the other hand, it gave a poor performance in a study performed by Sentelhas & Folegatti (2003) in a warm-humid environment in Brazil and another study in the humid tropical region of India by George (2012).

It can be concluded that the pan coefficient is very dependent on local and climatic conditions and should be determined by comparing the pan data with the FAO-56 PM ETo estimates (Chiew et al., 1995).

The values of RMSE, MBE, RE, MAE, and t-statistic used to evaluate the K_pan models for the monthly scale are given in Tables 4–8. The results in Tables 4–8 show that the Wahed & Snyder model performed better than other models, mainly from June to October. However, it gave poor performance in the rainy months (April, May). The Wahed & Snyder model had the smallest RMSE, RE, MAE, MBE, and t values from June to October among the models. All models showed varied relative errors (RE) by months (Table 6). According to models, RE as a percentage ranges from 5.5% to 54.4%. The Wahed & Snyder model errors ranged from 5.5% to 10.1% from June to October. The highest error happened in April at 28.4%. The Orang model showed the highest error, ranging from 37.2% to 54.4% from April to October (Table 6). The errors shown by other models during April-October were as follows: Snyder (10.3%–31%), Modified Snyder (9.7%–19.8%), Cuenca (9.8%–20.8%), Allen & Pruitt (10.2%–24.9%), Pereira (9.7%–23.1%), Raghuwanshi & Wallender (10.0%–22.3%).

As shown in Table 5, according to MBE values, K_pan models overestimated and underestimated mean ETo values according to months. Snyder and Raghuwanshi & Wallender models underestimated ETo values in April, but they overestimated ETo in other months. The Modified Snyder, Cuenca, and Pereira models underestimated ETo values in April and May. In contrast, these models overestimated ETo values in other months. Wahed & Snyder and Orang models underestimated ETo in all months.

In this study, monthly mean ETo values estimated by K_pan models ranged from 1.55 to 6.49 mm d⁻¹, whereas observed monthly mean ETo values ranged from 2.58 to 5.16 mm d⁻¹ (Table 9). The Wahed & Snyder model estimated the lowest monthly mean ETo with 2.41 mm d⁻¹ in October and the highest monthly mean ETo with 4.95 mm d⁻¹ in July. The Orang and Snyder models produced the least accurate monthly mean ETo estimates. The Wahed & Snyder model accurately estimated the monthly mean ETo in August. In addition, it showed good performance estimating ETo values in July, September, and October with small t values (4.705−4.870), as seen in Table 8. The Wahed & Snyder model had the smallest t values from July to October, whereas the Orang model had the highest t values during the season. Modified Snyder, Cueanca, Allen & Pruitt, Pereira, and Raghuwanshi & Wallender models accurately estimated the mean monthly ETo in May. Similarly, Irmak, Haman & Jones (2002), Gundekar, Khodke & Sarkar (2008), and Mahmud et al. (2020) indicated the success of K_pan models in accurately predicting ETo varied according to months.