Estimation of evapotranspiration and categorized ٢ maps of climate parameters applicable for civil and ٣ architectural designs ٤

Abstract: This study aims to estimate the potential evapotranspiration as well as to extract ١٢ categorized maps of climate parameters that are applicable for civil and architectural design . The ١٣ results showed that the Albrecht model estimates the potential evapotranspiration better than ١٤ other models in the most provinces of Iran. The best values of R ١٥ Brockamp-Wenner and Albrecht models in Bushehr (BU) and TE provinces, respectively. Finally, a ١٦ list of the best performance of each model has been presented. The best weather conditions (not ١٧ only for Iran but also for all countries) ١٨ MJ/m2/day, 12-26 °C, 18-30 °C, 5-21 ١٩ minimum temperature, and wind speed, respectively. The results are also useful for selecting the ٢٠ best model when researchers must apply humidity ٢١ addition, the designed maps and categories are applicable for considering the role of climatic ٢٢ parameters in architectural evaluations over Iran. ٢٣


Introduction ٢٧
The best estimations of actual evapotranspiration are obtained by using lysimeter or imaging ٢٨ techniques, the costs of which are very high ٢٩ become one modelling approach to estimate the potential evapotranspiration ٣٠ FAO Penman-Monteith (FPM) has been applied in various regions of the world ٣١ application requires many parameters which are often difficult to obtain. ٣٢ models have been developed for estimation of ٣٣ They include mass transfer, radiation, temperature, and pan evaporation ٣٤ transfer-based model is one of the most widely used models to estimate potential ٣٥ evapotranspiration. The common mass transfer ٣٦ Ivanov, Meyer,Trabert,and WMO [25 ٣٧ In the previous studies, one or more of the mass transfer ٣٨ with temperature, radiation, or pan evaporation ٣٩ models (temperature, radiation, or pan evaporation ٤٠ evapotranspiration better than the mass transfer ٤١ on specific (humid, arid, semiarid, etc.) weather conditions (that they aren't suitable for applying the ٤٢ mass transfer-based model) and/or didn't consider many methods ٤٣ Moreover, the results of previous studies are not useable for estimation of the potential ٤٤ This study aims to estimate the potential evapotranspiration as well as to extract maps of climate parameters that are applicable for civil and architectural design . The results showed that the Albrecht model estimates the potential evapotranspiration better than other models in the most provinces of Iran. The best values of R 2 were 0.9854 and 0.9826 for the Wenner and Albrecht models in Bushehr (BU) and TE provinces, respectively. Finally, a list of the best performance of each model has been presented. The best weather conditions (not only for Iran but also for all countries) to use mass transfer-based equations are 23.6 21 ℃, and 2.50-3.25 m.s -1 for solar radiation, mean, maximum, and minimum temperature, and wind speed, respectively. The results are also useful for selecting the when researchers must apply humidity-based models on the basis of available data. In addition, the designed maps and categories are applicable for considering the role of climatic parameters in architectural evaluations over Iran. humidity; Iran; linear regression; mass transfer; prevailing wind The best estimations of actual evapotranspiration are obtained by using lysimeter or imaging techniques, the costs of which are very high [1][2][3][4][5][6][7]. Thus, the FAO Penman-Monteith model become one modelling approach to estimate the potential evapotranspiration [9][10][11][12][13][14]. Although, the Monteith (FPM) has been applied in various regions of the world parameters which are often difficult to obtain. To this end, experimental models have been developed for estimation of the potential evapotranspiration using limited data. They include mass transfer, radiation, temperature, and pan evaporation-based model based model is one of the most widely used models to estimate potential evapotranspiration. The common mass transfer-based models include Papadakis, Rohwer, Dalton . or more of the mass transfer-based models have been compared with temperature, radiation, or pan evaporation-based models and in the most of the cases, other models (temperature, radiation, or pan evaporation-based models) estimated the potential spiration better than the mass transfer-based models. Because the previous studies focus on specific (humid, arid, semiarid, etc.) weather conditions (that they aren't suitable for applying the based model) and/or didn't consider many methods of mass transfer-based models. Moreover, the results of previous studies are not useable for estimation of the potential www.mdpi.com/journal/xxxx Estimation of evapotranspiration and categorized maps of climate parameters applicable for civil and archers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran This study aims to estimate the potential evapotranspiration as well as to extract maps of climate parameters that are applicable for civil and architectural design . The results showed that the Albrecht model estimates the potential evapotranspiration better than 854 and 0.9826 for the Wenner and Albrecht models in Bushehr (BU) and TE provinces, respectively. Finally, a list of the best performance of each model has been presented. The best weather conditions (not based equations are 23.6-24.6 for solar radiation, mean, maximum, and minimum temperature, and wind speed, respectively. The results are also useful for selecting the based models on the basis of available data. In addition, the designed maps and categories are applicable for considering the role of climatic humidity; Iran; linear regression; mass transfer; prevailing wind The best estimations of actual evapotranspiration are obtained by using lysimeter or imaging Monteith model [8] has . Although, the Monteith (FPM) has been applied in various regions of the world [15][16][17][18][19][20][21][22][23][24], its To this end, experimental the potential evapotranspiration using limited data. based models. The mass based model is one of the most widely used models to estimate potential Papadakis, Rohwer, Dalton, based models have been compared based models and in the most of the cases, other based models) estimated the potential based models. Because the previous studies focus on specific (humid, arid, semiarid, etc.) weather conditions (that they aren't suitable for applying the based models. Moreover, the results of previous studies are not useable for estimation of the potential evapotranspiration in other regions. Because they were recommended for one or more climatic ٤٥ conditions, but a climatic condition contains a wide range of magnitude of each weather parameter ٤٦ (e.g. temperature, relative humidity, wind speed, solar radiation, etc.) and results of each research ٤٧ (for a region with specific weather variations) is not applicable to other regions without determining ٤٨ specified ranges of each weather parameter even if climatic conditions (e.g. humid, arid, semi-arid, ٤٩ temperate, etc.) are identical for both regions. In addition, the governments cannot schedule for ٥٠ irrigation and agricultural water management when the potential evapotranspiration is estimated ٥١ for a basin, wetland, watershed, or catchment instead a state or province (different parts of them are ٥٢ located in more than one state or province) and/or number of weather station used is low (increasing ٥٣ uncertainty). Since, this study aims to estimate the potential evapotranspiration for 31 provinces of ٥٤ Iran (considering various weather conditions and useful for long-term and macroeconomic policies ٥٥ of governments) using average data of 181 synoptic stations (decreasing uncertainty) and by 11 mass ٥٦ transfer-based models to determine the best model based on the weather conditions of each province ٥٧ (for which ranges of weather parameters have been determined to use other regions and next ٥٨ researches). ٥٩ ٦٠

Materials and Methods ٦١
In this study, weather information (from 1986 to 2005) has been gathered from 181 synoptic ٦٢ stations of 31 provinces in Iran (without data gaps). Table 1 shows the position of each province and ٦٣ number of stations. ٦٤ Table 1 ٦٥ In each station, average of weather data in years measured has been considered as the value of ٦٦ that weather parameter in each month (e.g. value of relative humidity in July for North Khorasan ٦٧ (NK) is average of 20 data gathered). Finally, average of data in all stations has been considered as ٦٨ the value of that weather parameter in each month for provinces with more than one station (e.g.

٦٩
value of relative humidity in July for KH is average of 20×14=280 data gathered). All of the data ٧٠ mentioned have been used to estimate the potential evapotranspiration using 11 mass transfer-based ٧١ models and were compared with FPM model to determine the best model based on the weather ٧٢ conditions of each province (Table 2).

٧٣
Table 2 ٧٤ The best model for each province and the best performance of each model were determined ٧٥ using the coefficient of determination: ٧٦ In which, i indicates the month, ETFPM indicates the potential evapotranspiration calculated ٧٨ for FPM model, and ETm indicates the potential evapotranspiration calculated for mass ٧٩ transfer-based models.

٨٠
Finally, map of the annual average of solar radiation, mean, maximum, and minimum ٨١ temperature, relative humidity, and wind speed were provided and the best performance of each ٨٢ model based on these values was determined. Furthermore, the map of the best model for each ٨٣ province and the map of the error calculated for each province have been presented.

٨٤ ٨٥
3. Results and Discussion ٨٦ 3.1. Estimating the potential evapotranspiration for 31 provinces of Iran ٨٧ Table 3 shows the errors for each model and province. ٨٨ Table 3 ٨٩ According to the R2-values, each model estimates the potential evapotranspiration for only one ٩٠ or few provinces with very high accuracy. In the other words, preciseness of estimating by mass ٩١ transfer-based models is very sensitive to variations of the parameters used in each model (Table 2). ٩٢ ٩٣ 3.2. Comparison of the best models for each province ٩٤ Figure 1 compares the potential evapotranspiration using FPM with values estimated using the ٩٥ best method (based on Table 3) for each province.
According to Fig. 1 the Brockamp-Wenner for BU (R2=0.9854) yielded the best the potential ٩٨ evapotranspiration as compared to that from the FPM. However, the Albrecht has been introduced ٩٩ as the best model in the most of the provinces (23 provinces). In general, mass transfer-based models ١٠٠ are more suitable (R2 more than 0.97) for BU, HO (near the Persian Gulf), SK, KE, SB (south east of ١٠١ Iran) and TE, GI, and ES (south of Iran). However, according to Table 3, variations of the errors (the ١٠٢ worst and best R2) for different models are too high in all provinces; e.g. CB (0.839 and 0.9671 for the ١٠٣ Penman and Albrecht, respectively), BU (0.8932 and 0.9854 for the Papadakis and Albrecht, ١٠٤ respectively), SB (0.8846 and 0.9775 for the Papadakis and WMO, respectively), and HO (0.8083 and ١٠٥ 0.9742 for the Ivanov and Albrecht, respectively). These values indicate very different performance ١٠٦ of the mass transfer-based models for a specific weather condition in each province. For instance, the ١٠٧ Ivanov model estimates the potential evapotranspiration with the least R2 for HO and the greatest ١٠٨ R2 for EA than the other models. However, according to Table 2, the Ivanov model is a function of ١٠٩ mean temperature and relative humidity, the Papadakis is a function of minimum and maximum ١١٠ temperature and relative humidity, and the other models are a function of mean, minimum, and ١١١ maximum temperature, relative humidity, and wind speed. In addition, the only difference among ١١٢ the Albrecht, Dalton, Meyer, Rohwer, and WMO models is coefficients used in each model (Table 2) ١١٣ as well as the only difference among the Brockamp-Wenner, Mahringer, and Trabert models is also ١١٤ coefficients used in each model (Table 2). Thus we must use them according to their best weather ١١٥ conditions (with the most accuracy).

.3. Distinguishing various regions based on weather conditions ١١٨
The maps of the annual average of the weather parameters have been provided to detect the ١١٩ best conditions (range of weather parameters) that each model estimates the potential ١٢٠ evapotranspiration with maximum preciseness (Figs. 2 and 3). wind speed in all 31 provinces of Iran. As shown, value of solar radiation is more than 25.0 ١٢٦ MJ.m-2.day-1 for south of Iran, it is from 24.0 to 25.0 MJ.m-2.day-1 for centre of Iran, and it ranges ١٢٧ less than 24.0 MJ.m-2.day-1 for north of Iran. The mean temperature is less than 14 ℃ for north west ١٢٨ of Iran, it is more than 24 ℃ near the Persian Gulf, and it is from 14 to 24 ℃ for the other regions (with ١٢٩ the exception of NK and CB). The maximum temperature is more than 28.5 ℃ near the Persian Gulf, it ١٣٠ is from 25.5 to 27.0 ℃ for desert provinces, it is less than 19.5 ℃ for north west of Iran, and it is from ١٣١ 19.5 to 25.5 ℃ for the other regions. The minimum temperature is more than 17 ℃ near the Persian ١٣٢ Gulf, it is less than 7 ℃ for north west of Iran, it is from 11 to 15 near the Caspian Sea, and it is from 7 ١٣٣ to 13 ℃ for the other regions (with the exception of CB, NK, KE). The relative humidity is from 65 to ١٣٤ 70% near the Persian Gulf (with the exception of KH), it is from 50 to 65% in the north west and ١٣٥ north east of Iran (with the exception of AR), it is more than 70% near the Caspian Sea, and it is less ١٣٦ than 45% for other regions. The wind speed is from 2.50 to 3.50 m.s-1 for south east of Iran and near ١٣٧ the Persian Gulf, and it is from 1.25 to 2.75 m.s-1 for the other regions (with the exception of EA, AR, ١٣٨ GO, and CB). The wind speed plays an important role in architectural studies to design buildings ١٣٩ and structures with respect to the prevailing wind. For instance, in Qazvin, prevailing wind is a ١٤٠ south-eastern wind called Raz or Shareh [45][46]. This wind comes from desert areas of central Iran ١٤١ and is very warm and dry; hence it is reasonable that reduction of the WS due to desertification ١٤٢ approaches [47] leads to decreasing impacts of the mentioned climate and consequently reducing the ١٤٣ ETo. Therefore, the WS and may be introduced as the most influencing factors on variations of the ١٤٤ ETo in Qazvin.

١٤٥
The mass transfer-based models estimated the potential evapotranspiration in the south (near ١٤٦ the Persian Gulf) and south east of Iran (annual relative humidity 65-70% and <35%, respectively) ١٤٧ better than other provinces (Fig. 1). Therefore, the provinces of Iran are divided into five categories ١٤٨ (at least); (I) the provinces near the Persian Gulf (KH, BU, and HO), (II) the provinces of near the ١٤٩ Caspian Sea (GI, MZ, and GO), (III) the provinces of north east of Iran (WA, EA, AR, and ZA), (IV) ١٥٠ CB (due to the difference weather conditions than the near provinces), and (V) the other provinces.

١٥١
These categories are useful for future studies over Iran because these four parameters (light, ١٥٢ temperature, wind, and humidity) can employ to optimum design in architectural investigations.

١٥٣ ١٥٤
3.4. Determining a range of weather parameters for the best models ١٥٥ The maps of annual average of weather parameters (Figs. 2 and 3) are useful not only for the ١٥٦ mentioned categories, but also for determining the range of each parameter for which the best ١٥٧ preciseness of the mass transfer-based models is obtained (Table 4).

١٥٨
Table 4 ١٥٩ According to Table 4, the best performance of the Brockamp-Wenner, Mahringer, Meyer, ١٦٠ Trabert, and WMO models is in similar weather conditions (T=24-26 ℃, Tmax=28.5-30.0 ℃, ١٦١ Tmin=19-21 ℃, RH=65-70%, and u=3.00-3.25 m.s-1). However, the precise of them is different (e.g. ١٦٢ 0.9783 and 0.9854 for the WMO and Brockamp-Wenner models, respectively). This underlines the ١٦٣ important role of selection of the best model for a specified weather conditions. Furthermore, we can ١٦٤ see different ranges in the Albrecht, Dalton, Ivanov, Penman, Rohwer, and Papadakis models ( Table  ١٦٥ 4). Therefore, we can use the mass transfer-based models for other regions (in other countries) based ١٦٦ on Table 4 with respect to their errors. The best weather conditions to use mass transfer-based ١٦٧ equations are 23.6-24.6 MJ/m2/day, 12-26 ℃, 18-30 ℃, 5-21 ℃, and 2.50-3.25 m.s-1 (with the exception of ١٦٨ Penman) for solar radiation, mean, maximum, and minimum temperature, and wind speed, ١٦٩ respectively. Results are also useful for selecting the best model when researchers must apply ١٧٠ temperature-based models on the basis of available data. ١٧١ ١٧٢ 3.5. Comparison of the best models with their errors for each province ١٧٣ Figure 4 was plotted to detect the best model for each province versus its error (after ١٧٤ calibration). ١٧٥ Fig. 4  ١٧٦ First, although the Albrecht model is the most useful model for provinces of Iran (23 provinces), ١٧٧ but it is not suitable for 2 of the categories (near the Persian Gulf and north east of Iran) and east of ١٧٨ Iran (NK, RK, SK, and SB). This confirms that the categories are reliable and these 2 categories need ١٧٩ to more attention due to specific weather conditions. Moreover, the preciseness of the Albrecht ١٨٠ model is less than 0.98 in 18 provinces of Iran. It reveals that the Albrecht model is a general model ١٨١ for estimating the potential evapotranspiration (high application and fair preciseness). Thus, we ١٨٢ need to other temperature, radiation, and pan evaporation-based models to estimate the potential ١٨٣ evapotranspiration in these 18 provinces. For instance, values of solar radiation are more than 25.0 ١٨٤ MJ.m-2.day-1 for FA and KB, hence the radiation-based models may be useful for these provinces ١٨٥ [ [48][49][50][51][52][53][54]. It reveals that only if we use the mass transfer-based models for suitable (based on Table 4) ١٨٦ and specific (based on Figs. 2 and 3) weather conditions, the highest preciseness of estimating will be ١٨٧ obtained.

١٨٨ ١٨٩
Conflicts of Interest: The authors declare no conflict of interest.

٢٠٠
Δ is the slope of the saturation vapour pressure-temperature curve (kPa/℃)

٢٠١
T is the average daily air temperature (℃) ٢٠٢ u is the mean daily wind speed at 2 m (m/s)

٢٠٣
H is the elevation (m), φ is the latitude (rad)

٢٠٤
Tmin is the minimum air temperature (℃)

٢٠٥
Tmax is the maximum air temperature (℃)

٢٠٦
RH is the average relative humidity (%)

٢٠٧
n is the actual duration of sunshine (hr)

٢٠٨
Rs is the solar radiation (MJ/m 2 /day) ٢٠٩ ema is the saturation vapour pressure at the monthly mean daily maximum temperature (kPa)

٢١٠
٢١١  T is the average daily air temperature (℃), u is the mean daily wind speed at 2 m (m/s), ٢١٨ T min is the minimum air temperature (℃), T max is the maximum air temperature (℃), and ٢١٩ RH is the average relative humidity (%) ٢٢٠