Comparison of Different Models in Estimating Standard Evapotranspiration in Lampung Province, Indonesia

Evapotranspiration (ET) is the loss of water to the atmosphere by combined processes of evaporation from soil and plant surfaces and transpiration from plants. Since various factors affect ET, including weather, crops and soil parameters; numerous equations have been developed to quantify standard ET. The equations vary in data requirements from very simple, empirically based or simplified equations to complex, more physically based equations. This study used six methods in estimating standard evapotranspiration using data from September 2011‒August 2012 from Climate Station at Masgar (05o10'20” S, 105o10' 49”E, 50 m dpl) Lampung, Indonesia. The six models are: Hargreaves-Samani 1985 (H/S), FAO 24 Radiation (24RD), FAO 24 Blaney-Criddle (24BC), FAO 24 Pan Evaporation (24PAN), Linacre (Lina), and Makkink (Makk). The results were analyzed using statistics methods in error indicators, which are: Root Mean Square Error(RMSE), Mean Absolute Error (MAE), and Logaritmic Root Mean Square Error(LOG RMSE), while the closeness among the models was analyzed using Index Agreement (IA). Direct measurement had been done using lysimeters (3x2x1) m. The study concluded that Makkink model is the suitable simple model that should be chosen in Lampung lowland area to calculate ETo when climate data is limited, besides the recommended FAO 56 Penman Monteith.


INTRODUCTION
Evaporation is the main component in hydrology cicle, therefore, accurate estimation of evaporation rate is important for water management and eventually for agriculture production. However, it is difficult to measure evaporation rate directly since evaporation affected by various factors. Evaporation is affected by climate factors such as solar radiation, air temperature and humidity and wind velocity; by crops type and environment and by soil condition and management (Temesken, Davidov and Frame, 2005). Since those factors are linked to each other and change in time and space, it is difficult to develop equation for estimating evaporation rate for various crops on different condition. Therefore, a scheme called reference evapotranspiration was developed. Reference ET is defined as ''the rate of evapotranspiration from an extensive area of 0.08-0.15 m high, uniform, actively growing, green grass that completely shades the soil and is provided with unlimited water and nutrients'' (Bakhtiari et al., 2011). More recently, Allen et al. (1998) elaborated on the concept of ETo, referring to an ideal 0.12 m high crop with a fixed surface resistance of 70 s m -1 and an albedo of 0.23. Several equations has been developed to estimate the reference evapotranspiration; some of that were derived based on physical processes of the evapotranspiration but mostly are empirical based on ststistical relationship between evapotranspiration and one or more climate variables (Berengena and Gavilan, 2005). Approaching methods to estimate evapotranspiration rate was developed increasingly in the last 30 years such as based on air temperature measurement (Hargraeves and Sumani, 1985), based on solar radiation Priestly and Taylor method (Priestly and Taylor, 1972) and based on combination of radiation balance and air moisture aerodynamic movement (Penman, 1948). Penman method has been improved several times such as Penmann method modified by Monteith and known as Penman-Monteith equation (Monteith, 1965) approach method in FAO 24 version (Doorenbos and Pruitt, 1977), FAO 56 modification (Allen, 1998)  It also showed that estimation using Penman Monteith method in general gave higher rate than Pan A measurement. Lampung Province (103 0 40' -105 0 50' E; and between: 6 0 45' -3 0 45' S;35.288,35 km 2 ) is located at Southeast tip of Sumatra Island, Indonesia. Lampung climate is characterized by monsoonal rain distribution and local characteristics. Rain season in general is from October to March with the peak on January/February and dry season is from April to September . Monthly rainfall ranges from 50 -200 mm and annual rainfall ranges from 1200 mm (lowland area) to 2500 mm (highland area). Lampung economic is dominated by agriculture products mainly coffee, chocolate, rubber and sugarcane. Lampung is also considered as main area for cash crops such as paddy, soybean and Maize. Therefore, finding good and reliable method in estimating crops water requirement is necessary for better agriculture management. The objective of this research was to find a closest model to the FAO 56 PM model by comparing six different models in estimating standard evapotranspiration in Lampung area, Indonesia. Error (LOG RMSE), while the closeness among the models was analyzed using Index Agreement (IA). Finally, the results were compared to the direct measurement using 3 lysimeters (3x2x1 m) planted with Sporobulus diander grass.

II. METHODS
2.1 Description of Models 2.1.1 Hargreaves-Samani 1985 (H/S) (Hargreaves and Samani, 1985) The equation of this model is: with ETo is standard evapotranspiration (mm/day), is daily mean temperature (ᵒC), is maximum temperature(ᵒC), is minimum temperature, dan is radiation on top of the atmosfer (MJ/m 2 /day).

FAO 24 Radiation (24RD) (Doorenbos and Pruitt, 1977)
The equation of this model is: ETo is standard evapotranspiration (mm/day), ∆vapor pressure curve (kPa/ o C),γ is psychrometric constant (kPa/ o C), is solar radiation(MJ/m 2 /day), a and b conversion factor with = −0.3 mm/day and derived from the equation: ETo is standard evapotranspiration (mm/day), P is percentage of day length, T is daily average temperature (˚C), RH is minimum relative humidity (%), n/N is ratio of possible actual day, Ud is wind speed at 2 m (m/s)

FAO 24 Pan Evaporation (24PAN) Doorenbos and
Pruitt (1977) The equation of this model is ETo is standard evapotranspiration (mm/day), is pan coefficient, is class A Pan evaporation (mm/day), 2 is average wind speed (m/s), relative humidity (%), dan is distance between pan and green crops (m).
2.1.5 Linacre (LINA) (Linacre, 1977) The equation of this model is: is standard evapotranspiration (mm/day) is mean temperature (ᵒC), is latitude of the climate station (ᵒ), is elevation of climate station (m), dan is average dew point temperature (°C). equation is: is average dew point temperature (°C), is mean temperature (ᵒC), dan is average daily relative humidity (%).

Statistical analysis
The statistical analysis from daily evapotranspiration data including the error indicator of each model compare to the FAO 56 PM as the standard is presented in Table 2    is a coefficient, 0.16 for interior land area and 0.19 for coastal area, is top solar radiation (MJ/m 2 /day). Basically, this model can be calculated using only maximum and minimum temperature (ᵒC) which is more available in most research stations. Irmak, Allen and Whitty (2003) conducted a research using daily measured weather data for a 23-year (1978-2000) in North-Central Florida to examine twenty one ET0 methods (excluding the FAO 56-PM; 10 combination methods, 4 radiation methods, 5 temperature methods and 2 pan evaporation methods) and the results showed that the performance of all radiation methods including Makkink was poorer than that of all combination methods except the Stephens-Stewart method, which performed better than the original PM combination method. Makkink methods had a similar standard error of estimate for all months with the Stephens-Stewart method, but the method significantly underestimated ET0 throughout the year. The tendency to underestimate high evaporative demand in Makkink model has been found in most of previous studies e.g. in Korea , in Germany (Xu and Chen, 2005) in Jordan (Mohawesh, 2011)  3.2. Comparing Makkink model with direct measurement Direct evapotranspiration measurement was done using lysimeters. Measuring water input and out put together with soil water content on the lysimeters was a challenge. During this research the measurements were repeated several times, however due to technical problems they were not always done in the same day. Therefore, the results (Table 7 and 8) were considered as an average number.
In average from Table 7 and 8, evapotranspiration rate during the research was 3.8 +1.11 = 4.91 mm/day, higher than estimated Makkink (3.306 mm) and FAO (3.533 mm) ( Table 6). In general, the average and accumulation of observed Pan A gave slightly higher evapotranspirasion compared to estimated Makkink. However, observed Pan A had much wider standard deviation; Makkink model gave more flat result in daily estimation while Pan A was more fluctuative.

IV. CONCLUSION
This study concluded that Makkink model is a simple model that can be chosen in Lampung as an alternative to estimate standard evapotranspiration in an area with limited climate data needed to apply FAO 56 PM, with a note that Makkink tended to be underestimated during dry months. Estimation of evapotranspiration using models are sufficient for averaged and accumulated result from some period of time, not for daily or single measuremnt.