**Evapotranspiration of Succulent Plant** *(Sedum aizoonvar.floibundum)*

A. Al-Busaidi, T. Yamamoto, S. Tanak and S. Moritani

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/53213

### **1. Introduction**

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[9] Kobayashi, T, Matsuda, S, Nagai, H, & Teshima, J. (2001). A bucket with a bottom hole (BBH) model of soil hydrology. In: Soil-Vegetation-Atmosphere Transfer Schemes and Large-Scale Hydrological Models (ed. by H. Dolman et al.), IAHS Publ. 270. IAHS Press,

[10] Teshima, J, Hirayama, Y, Kobayashi, T, & Cho, H. Estimating evapotranspiration from a small area on a grass-covered slope using the BBH model of soil hydrology. *J. Agric.*

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[13] Zhan, Ch.-S, Xia, J, Chen, Z, & Zuo, Q.-T. (2008) An integrated hydrological and meteorological approach for the simulation of terrestrial evapotranspiration. Hydrol.

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240 Evapotranspiration - An Overview

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in 30 years), *Advances in water resources* 17 (1994), 3-18.

Fresh water resources available for agriculture are declining quantitatively and qualitative‐ ly. Therefore, the use of less water or lower-quality supplies will inevitably be practiced for irrigation purposes to maintain economically viable agriculture. Globally arid and semiarid areas are facing salinization of soils along with the acute shortage of water resources. The utilization of marginal waters for agriculture is getting considerable importance in such re‐ gions. In hot and dry climate, one of the most successful ground covers is Sedum. It is per‐ ennial plant, which grows by natural moisture even if there is a little soil [1]. As their common name of stonecrop suggests, they do very well in rocky areas, surviving on little soil and storing water in their thick leaves. While some do well in very sunny areas, others thrive in shade and they all tend to like good drainage. Sedums are suitable plants for rock gardens and flower borders. They are very easy to propagate as almost any tiny leaf or piece of stem that touches the ground will root. Some types become rather invasive but are easy to control since the roots are never very deep [1].

Sedum is one of the promising plants in dry areas. It has the characteristics of fire preven‐ tion and dry resistance. It has low transpiration value in the daytime compared to other plants. It uses latent heat transmission to control water loss. Generally, succulents, such as Sedum, have been the most studied and used plants for green roofs [2-5]. Greenroofs are in‐ creasingly being used as a source control measure for urban storm water management as they detain and slowly release rainwater. Their implementation is also recognized as having other benefits, including: habitat creation for birds and insects [6] filtering of aerosols; ener‐ gy conservation by providing thermal insulation [7, 8]; improvement of local microclimate through evaporation; reduction of rooftop temperatures [8]. One of the main reasons Se‐

© 2013 Al-Busaidi et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Al-Busaidi et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

dums seem ideally suited to green roof cultivation is the fact that many possess Crassula‐ cean acid metabolism (CAM). During periods of soil moisture deficit, CAM plants keep their stomata closed during the day when transpiration rates are normally high and open them at night when transpiration rates are significantly lower. This is in contrast to C3 and C4 plants, which do not keep their stomata closed during the day and therefore have higher water use rates than CAM plants.

**Soil properties**

> Powder Pearlite

Coarse Pearlite

*Growth chamber study*

midity were 20 o

**Table 1.** Soil physicochemical properties

**Sand (%) Silt**

**(%)**

**Clay (%) Bulk**

**density (gcm-3)**

**S. Hydraulic Conductivity (cm/s)**

98.6 1.4 0 0.19 3.2×10-1 0.8 - - -

100 0 0 0.10 5.6×10-1 - - - -

KS 89.6 5.8 4.6 0.48 3.6×10-2 40.4 12.0 0.96 12.4 VS 92.9 1.7 5.4 0.67 9.2×10-1 12.5 1.0 0.09 10.7

Sand 96.1 0.4 3.5 1.42 3.4×10-2 1.5 0.12 0.02 5.9 Touhaku 53.9 17.8 28.3 1.11 5.8×10-4 9.5 0.50 0.09 5.4

Plastic containers of 15 cm height and 22 cm diameter were filled up to 10 cm height with different types of soils. The physicochemical properties of the used soils were same as the soils used in glasshouse study (Table 1). Sedum plant was transplanted in each pot with in‐ tensity of 30 plants/pot. All soils were irrigated until the field point of pF 1.8. After 24 hours, the evaporation process was inhibited by covering soil surface with plastic sheet. All pots

midity and light of 10000 Lux. Whereas, at the night time, the temperature and relative hu‐

All used soils were air dried and passed through 2 mm sieve. Soil texture was determined by pipette method. Cation exchange capacity (CEC) was determined by atomic absorption

C and 60 %, respectively. All pots were placed in weighing balance scale so

were transferred to growth chamber with a day time temperature of 40 o

water lost by transpiration process was monitored (Figure 1).

**Figure 1.** Weighing balance for transpiration measurements

*Physicochemical analysis*

**CEC (cmol(+)/kg)**

Evapotranspiration of Succulent Plant *(Sedum aizoonvar.floibundum)*

**C (%) N (%) C/N**

http://dx.doi.org/10.5772/53213

243

C, 60 % relative hu‐

Research that examines the growth obstruction moisture point in Sedum is little, and its growth is confirmed as for the amount of pF 3.0 or lower moisture content [9, 10]. Sedum has the characteristic of doing shutting transpiring control and when plant under water stress conditions, carbon dioxide is absorbed at nighttime which also common in some Cras‐ sulaceous plants that have Crassulaceous Acid Metabolism (CAM). For terrestrial plant spe‐ cies CAM is generally considered to be an adaptation to growth in dry environments [11, 12]. CAM species generally have high water use efficiencies and slow growth rates and are most abundant in arid regions and dry microhabitats. The degree of CAM expression (the proportion of nighttime CO2 assimilation by PEP carboxylase) potentially may vary from CO2 uptake only at night, to CO2 uptake both at night and during daylight, to CO2 uptake only during the day. A greater proportion of nighttime CO2 uptake has been associated with greater water use efficiency. This phenomenon helps Sedum to save much water and keep it for longer time. Sedum is a drought tolerant plant and its growth and survival under very dry conditions, still not well known. Therefore, objective of this study was to evaluate the ability of Sedum plant to grow under different soils condition where evapotranspiration was the main indicator for plant interaction with dry conditions. In addition, the studies on the growth and survival of Sedum under saline water conditions are scanty and not well documented. Therefore, the other objective of the study was to evaluate Sedum growth un‐ der saline water irrigation either by surface or shower method.

### **2. Materials and methods**

#### *Glasshouse study*

Plot experiment was carried out in a glasshouse at Arid Land Research Center of Tottori University, Japan. The plots were made in two directions (North & South) with a slope of 20 and 30 degree, respectively. Twelve plots were filled up to 10 cm thickness with five types of soils (Table 1). The used soils have different criteria in which four of them were artificial and the other two were sandy and clayey soils. Sedum (*Sedum aizoonvar.floibundum*) plants were transplanted uniformly in all types of soils. Plants were irrigated by sprinkler with intensity of 20 mm/h. Air temperature, relative humidity and solar radiation were measured continu‐ ously day and night by Hobo (Pro series, onset, USA) meter. Evaporation and evapotranspi‐ ration were measured by using micro-lysimeters and evaporation pan (class A) following pan evaporation method (ETo = Epan \* Kpan, ETp= ETo \* Kc) where ETo: reference evapotranspi‐ ration, Epan: pan evaporation, Kpan: pan coefficient, ETp: potential evapotranspiration, Kc: crop factor [13].


#### **Table 1.** Soil physicochemical properties

#### *Growth chamber study*

dums seem ideally suited to green roof cultivation is the fact that many possess Crassula‐ cean acid metabolism (CAM). During periods of soil moisture deficit, CAM plants keep their stomata closed during the day when transpiration rates are normally high and open them at night when transpiration rates are significantly lower. This is in contrast to C3 and C4 plants, which do not keep their stomata closed during the day and therefore have higher

Research that examines the growth obstruction moisture point in Sedum is little, and its growth is confirmed as for the amount of pF 3.0 or lower moisture content [9, 10]. Sedum has the characteristic of doing shutting transpiring control and when plant under water stress conditions, carbon dioxide is absorbed at nighttime which also common in some Cras‐ sulaceous plants that have Crassulaceous Acid Metabolism (CAM). For terrestrial plant spe‐ cies CAM is generally considered to be an adaptation to growth in dry environments [11, 12]. CAM species generally have high water use efficiencies and slow growth rates and are most abundant in arid regions and dry microhabitats. The degree of CAM expression (the proportion of nighttime CO2 assimilation by PEP carboxylase) potentially may vary from CO2 uptake only at night, to CO2 uptake both at night and during daylight, to CO2 uptake only during the day. A greater proportion of nighttime CO2 uptake has been associated with greater water use efficiency. This phenomenon helps Sedum to save much water and keep it for longer time. Sedum is a drought tolerant plant and its growth and survival under very dry conditions, still not well known. Therefore, objective of this study was to evaluate the ability of Sedum plant to grow under different soils condition where evapotranspiration was the main indicator for plant interaction with dry conditions. In addition, the studies on the growth and survival of Sedum under saline water conditions are scanty and not well documented. Therefore, the other objective of the study was to evaluate Sedum growth un‐

Plot experiment was carried out in a glasshouse at Arid Land Research Center of Tottori University, Japan. The plots were made in two directions (North & South) with a slope of 20 and 30 degree, respectively. Twelve plots were filled up to 10 cm thickness with five types of soils (Table 1). The used soils have different criteria in which four of them were artificial and the other two were sandy and clayey soils. Sedum (*Sedum aizoonvar.floibundum*) plants were transplanted uniformly in all types of soils. Plants were irrigated by sprinkler with intensity of 20 mm/h. Air temperature, relative humidity and solar radiation were measured continu‐ ously day and night by Hobo (Pro series, onset, USA) meter. Evaporation and evapotranspi‐ ration were measured by using micro-lysimeters and evaporation pan (class A) following pan evaporation method (ETo = Epan \* Kpan, ETp= ETo \* Kc) where ETo: reference evapotranspi‐ ration, Epan: pan evaporation, Kpan: pan coefficient, ETp: potential evapotranspiration, Kc:

der saline water irrigation either by surface or shower method.

water use rates than CAM plants.

242 Evapotranspiration - An Overview

**2. Materials and methods**

*Glasshouse study*

crop factor [13].

Plastic containers of 15 cm height and 22 cm diameter were filled up to 10 cm height with different types of soils. The physicochemical properties of the used soils were same as the soils used in glasshouse study (Table 1). Sedum plant was transplanted in each pot with in‐ tensity of 30 plants/pot. All soils were irrigated until the field point of pF 1.8. After 24 hours, the evaporation process was inhibited by covering soil surface with plastic sheet. All pots were transferred to growth chamber with a day time temperature of 40 o C, 60 % relative hu‐ midity and light of 10000 Lux. Whereas, at the night time, the temperature and relative hu‐ midity were 20 o C and 60 %, respectively. All pots were placed in weighing balance scale so water lost by transpiration process was monitored (Figure 1).

**Figure 1.** Weighing balance for transpiration measurements

#### *Physicochemical analysis*

All used soils were air dried and passed through 2 mm sieve. Soil texture was determined by pipette method. Cation exchange capacity (CEC) was determined by atomic absorption spectrophotometer (Model Z-2300 Hitachi corp, Japan) after leaching with ammonium ace‐ tate solution and using sodium acetate as an index cation. Saturated hydrolyic conductivity was measured by constant head method. Whereas, percentage N and C were measured by C/N coda (MT700, Yanagimoto, Japan). The pF values for soil moisture characteristic curve were measured by suction and centrifuge methods for pF values of 0 - 4.2 and Saicromatar method for 4.2 - 6.0 (Figure 2). The selected properties of the soils are given in Table 1.

soil can keep and the plant can take which usually related to soil water plant interactions. From Figure 2, it can be seen that Touhaku soil got the highest values for water content fol‐ lowed by K soil. That usually related to clay and silt contents in the soil. Moreover, as sand particles increase, volumetric water content decrease and that was the case with perlite and

Evapotranspiration of Succulent Plant *(Sedum aizoonvar.floibundum)*

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245

During the study period, the weather was changing with the average glasshouse tempera‐

transpiration (ET) process (Figure 3). Comparing ET values for both slopes of glasshouse study, it wasn't a big difference in the water lost between both slopes. However, there was a big difference between soil types (Figures 3-4) and that mainly related to the physiochemical properties of each soil. Generally, it can be noticed that after irrigation the water loss was high and gradually decreased with time. It is ranking in the following order: V soil > K soil > Sand >Touhaku> Pearlite. Moreover, it can be seen that Touhakusoil got the highest value for mean ET (Figure 4). Whereas, Pearlite soil got the lowest values. This can be related to the soil physical properties in which Touhakusoil has much clay content that can keep much water that could be subjected to ET losses. In same time, it was encouraging plant growth and plant lost much water through transpiration process compared to other soils. For Pearlite soil, since it has coarse particles so most water was lost through drainage and the rest of water was used for plant growing mechanisms. However, water lost from different slopes and directions (North

Since ET is one of the growth indicators, it seems that plant growing in K, V andTouhaku soils was growing very good by giving high values for ET. Whereas, plant growing in Pear‐

C and 74 %, respectively. Average value of temperature seems to be

C could enhance water loss through evapo‐

sand dune soils.

**Figure 2.** Soil water retention curve of studied soils

suitable for Sedum growth but high value of 35 o

and South) was inconsistence and was changing with time.

lite soil was saving the water and reduce ET process (Figure 3 & 4).

ture and humidity of 29 o

### *Salinity study*

Pot experiment was carried out in same glasshouse at Arid Land Research Center, Tottori University, Japan. Sand dune soil was placed in 4 L pots. Sedum *(Sedum aizoon var. floibun‐ dum)* was planted in 24 pots at the planting density of 4 plants per pot. One group of the pots was irrigated with the saline water directly on the surface of the soil and the other group of pots was showered by the same water treatments. Irrigation with saline water was started after 14 days of planting. Saline water treatments were consisted of four levels:


Sea water was diluted by tap water to achieve these ECw levels of irrigation water. Four sal‐ ine water treatments were combined with two types of irrigation methods e. g., surface or normal irrigation (N) and shower or sprinkler irrigation (S). These treatments are denoted as 0.7(N), 0.7(S), 15(N), 15(S), 30(N), 30(S), 46(N), and 46(S) respectively. Plants were irrigated twice a week depending on the loss of evapotranspiration (ETc) which was estimated by gravitational measurement. Extra water at the rate of 10% was added for leaching purpose. Evaporation was measured by using evaporation pan (class A). Air temperature and relative humidity were measured during the day as well as night by Hobo meter (Pro series, onset, USA). Prior to the harvesting of the plants for their fresh and dry weight, plant height and leaf area (by portable area meter LI-3000A) were also measured. Post-harvest soil samples were collected from each pot at a depth of 0-20 cm. Soil electrical conductivity (EC) was measured in the 1: 5 soil-water suspensions. Data were analyzed statistically for analysis of variance (ANOVA) and the means were compared at the probability level of 5% using least significant difference (LSD) test [14].

### **3. Results and discussion**

#### *Glasshouse study and Soil characteristics*

Table 1 details the properties of the studied soils. All of them contain high percentage of sand particles with varied values of bulk density and saturated hydraulic conductivity. By checking cation exchange capacity (CEC) and C/N values, it seems that KS, VS and Touhaku soils are the most fertile soils. Generally, the physiochemical properties of these soils sup‐ port plant growth but survival time or drought effect dependson how much moisture the soil can keep and the plant can take which usually related to soil water plant interactions. From Figure 2, it can be seen that Touhaku soil got the highest values for water content fol‐ lowed by K soil. That usually related to clay and silt contents in the soil. Moreover, as sand particles increase, volumetric water content decrease and that was the case with perlite and sand dune soils.

**Figure 2.** Soil water retention curve of studied soils

spectrophotometer (Model Z-2300 Hitachi corp, Japan) after leaching with ammonium ace‐ tate solution and using sodium acetate as an index cation. Saturated hydrolyic conductivity was measured by constant head method. Whereas, percentage N and C were measured by C/N coda (MT700, Yanagimoto, Japan). The pF values for soil moisture characteristic curve were measured by suction and centrifuge methods for pF values of 0 - 4.2 and Saicromatar method for 4.2 - 6.0 (Figure 2). The selected properties of the soils are given in Table 1.

Pot experiment was carried out in same glasshouse at Arid Land Research Center, Tottori University, Japan. Sand dune soil was placed in 4 L pots. Sedum *(Sedum aizoon var. floibun‐ dum)* was planted in 24 pots at the planting density of 4 plants per pot. One group of the pots was irrigated with the saline water directly on the surface of the soil and the other group of pots was showered by the same water treatments. Irrigation with saline water was started after 14 days of planting. Saline water treatments were consisted of four levels:

Sea water was diluted by tap water to achieve these ECw levels of irrigation water. Four sal‐ ine water treatments were combined with two types of irrigation methods e. g., surface or normal irrigation (N) and shower or sprinkler irrigation (S). These treatments are denoted as 0.7(N), 0.7(S), 15(N), 15(S), 30(N), 30(S), 46(N), and 46(S) respectively. Plants were irrigated twice a week depending on the loss of evapotranspiration (ETc) which was estimated by gravitational measurement. Extra water at the rate of 10% was added for leaching purpose. Evaporation was measured by using evaporation pan (class A). Air temperature and relative humidity were measured during the day as well as night by Hobo meter (Pro series, onset, USA). Prior to the harvesting of the plants for their fresh and dry weight, plant height and leaf area (by portable area meter LI-3000A) were also measured. Post-harvest soil samples were collected from each pot at a depth of 0-20 cm. Soil electrical conductivity (EC) was measured in the 1: 5 soil-water suspensions. Data were analyzed statistically for analysis of variance (ANOVA) and the means were compared at the probability level of 5% using least

Table 1 details the properties of the studied soils. All of them contain high percentage of sand particles with varied values of bulk density and saturated hydraulic conductivity. By checking cation exchange capacity (CEC) and C/N values, it seems that KS, VS and Touhaku soils are the most fertile soils. Generally, the physiochemical properties of these soils sup‐ port plant growth but survival time or drought effect dependson how much moisture the

*Salinity study*

244 Evapotranspiration - An Overview

**i.** fresh water (0.7 dS m-1),

significant difference (LSD) test [14].

*Glasshouse study and Soil characteristics*

**3. Results and discussion**

**iii.** highly saline (30 dS m-1), and iv) sea water (46 dS m-1).

**ii.** saline (15 dS m-1),

During the study period, the weather was changing with the average glasshouse tempera‐ ture and humidity of 29 o C and 74 %, respectively. Average value of temperature seems to be suitable for Sedum growth but high value of 35 o C could enhance water loss through evapo‐ transpiration (ET) process (Figure 3). Comparing ET values for both slopes of glasshouse study, it wasn't a big difference in the water lost between both slopes. However, there was a big difference between soil types (Figures 3-4) and that mainly related to the physiochemical properties of each soil. Generally, it can be noticed that after irrigation the water loss was high and gradually decreased with time. It is ranking in the following order: V soil > K soil > Sand >Touhaku> Pearlite. Moreover, it can be seen that Touhakusoil got the highest value for mean ET (Figure 4). Whereas, Pearlite soil got the lowest values. This can be related to the soil physical properties in which Touhakusoil has much clay content that can keep much water that could be subjected to ET losses. In same time, it was encouraging plant growth and plant lost much water through transpiration process compared to other soils. For Pearlite soil, since it has coarse particles so most water was lost through drainage and the rest of water was used for plant growing mechanisms. However, water lost from different slopes and directions (North and South) was inconsistence and was changing with time.

Since ET is one of the growth indicators, it seems that plant growing in K, V andTouhaku soils was growing very good by giving high values for ET. Whereas, plant growing in Pear‐ lite soil was saving the water and reduce ET process (Figure 3 & 4).

In this study, plants were irrigated at the beginning of the study and soil surface was sealed so the only way to loss water was through transpiration process. Amount of transpiration water usually depend on plant growth and available soil moisture content. In CAM plants the transpiration process usually increase with day time and decrease at night. In this study the plant was under water stress condition so soil water content was decreasing with time. In the first day, since there was much water, plant was losing much water in the day time compared to night time (Figure 5). Whereas, at the last day of the study (Figure 6), plant was under stress and was losing less water in the day compared to the night time. This phenom‐ enon usually happen in CAM plants when they are under stress condition. Under heat and water stress condition plants were trying to save much water by closing their stomata and opening them at normal conditions. This phenomenon can be seen very clear in Figure 6.

Evapotranspiration of Succulent Plant *(Sedum aizoonvar.floibundum)*

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247

Generally Sedum plant is keeping much water in their leaves and since the plant was get‐ ting much water in the first day so it was losing much water in the day and night time (Figure 5) but in the last day (Figure 6) water lost was low and transpiration rate was almost

constant in which the plant was keeping constant water potential value [10].

**Figure 5.** Transpiration ratio at early stage of study

**Figure 6.** Transpiration ratio at late stage of study

**Figure 3.** Irrigation and evapotranspiration values of Sedum in glasshouse study

**Figure 4.** Mean values for Sedum evapotranspiration in glasshouse study

#### *Growth chamber study*

Growth chamber is a controlled environment and what happened inside the chamber can be more understandable than outside environment. In this study, Sedum transpiration ratio was continuously monitored by weighing scale (Figures 5-6). Day time was considered from 0-12 o'clock and night time from 12-24 o'clock. Figure 5 represent transpiration ratio at the first day of study. It can be seen that plants grown in V, K and sand soils got the highest transpiration values among others. Whereas, plants in Pearlite and PP soils got the lowest values in both intervals. This can be related to the soil physical properties which supply wa‐ ter to plants. Pearlite and PP are coarse soils with particle size of 3 and 1 mm, respectively, in which most water in the soil was in vapor form and not directly available for the plant. Whereas, K and V soils have high values of clay and silt contents and that increasedwater holding capacity compared to others.

In this study, plants were irrigated at the beginning of the study and soil surface was sealed so the only way to loss water was through transpiration process. Amount of transpiration water usually depend on plant growth and available soil moisture content. In CAM plants the transpiration process usually increase with day time and decrease at night. In this study the plant was under water stress condition so soil water content was decreasing with time. In the first day, since there was much water, plant was losing much water in the day time compared to night time (Figure 5). Whereas, at the last day of the study (Figure 6), plant was under stress and was losing less water in the day compared to the night time. This phenom‐ enon usually happen in CAM plants when they are under stress condition. Under heat and water stress condition plants were trying to save much water by closing their stomata and opening them at normal conditions. This phenomenon can be seen very clear in Figure 6.

Generally Sedum plant is keeping much water in their leaves and since the plant was get‐ ting much water in the first day so it was losing much water in the day and night time (Figure 5) but in the last day (Figure 6) water lost was low and transpiration rate was almost constant in which the plant was keeping constant water potential value [10].

**Figure 5.** Transpiration ratio at early stage of study

**Figure 3.** Irrigation and evapotranspiration values of Sedum in glasshouse study

**Figure 4.** Mean values for Sedum evapotranspiration in glasshouse study

Growth chamber is a controlled environment and what happened inside the chamber can be more understandable than outside environment. In this study, Sedum transpiration ratio was continuously monitored by weighing scale (Figures 5-6). Day time was considered from 0-12 o'clock and night time from 12-24 o'clock. Figure 5 represent transpiration ratio at the first day of study. It can be seen that plants grown in V, K and sand soils got the highest transpiration values among others. Whereas, plants in Pearlite and PP soils got the lowest values in both intervals. This can be related to the soil physical properties which supply wa‐ ter to plants. Pearlite and PP are coarse soils with particle size of 3 and 1 mm, respectively, in which most water in the soil was in vapor form and not directly available for the plant. Whereas, K and V soils have high values of clay and silt contents and that increasedwater

*Growth chamber study*

246 Evapotranspiration - An Overview

holding capacity compared to others.

**Figure 6.** Transpiration ratio at late stage of study

#### *Transpiration ratio assumption*

In case of water stress, evapotranspiration could be a good indicator for plant survival. In this study cumulative transpiration and ET were related to square roots of elapse time (Fig‐ ure 7). Both studies in glasshouse and growth chamber were agreed with starting point but with the time, each study gave different patterns especially in the last days of measure‐ ments. This can be related to the environmental conditions of both studies. Glasshouse con‐ ditions were varied and both evaporation and transpiration were counted. In same time plant was growing under normal condition without any heat or drought stresses. Whereas, in growth chamber, the growth conditions were almost constant and transpiration was the main factor that was measured. In addition plant was growing under stress condition in which transpiration was decreasing with time. However, all values in growth chamber were highly correlated with R2 value of 0.99. This finding was also confirmed by Moritaniet al. [9] and Iijima [10].

whereα, β, γ, and δ are fitting parameters. Root mean square error (RMSE) was calculated

*RMSE*

2 1 *n <sup>i</sup> <sup>i</sup> d*

<sup>=</sup> <sup>=</sup> å (2)

Evapotranspiration of Succulent Plant *(Sedum aizoonvar.floibundum)*

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249

*N*

where d is the difference between observed and calculated values and N is the total number of the data. The average value for RMSE is 0.0097 which mean there is a good fit between observed and calculated data. It can be seen that K and V soils were giving different graphs depending on physicochemical properties of each soil. Point 1 and point 2 are the changing points. A decrease of 10 % from highest point in the graph is a representation of point 1 and an increase by 10 % from lowest point is a representation for point 2. Many points were checked and 10 % of increase or decrease was giving the best data and matching with value of changing point. The best values for point 1 were found in K soil followed by Touhaku > V > Pearlite > Sand > PP soils. For point 2 the order is Touhaku > K > V > Pearlite > Sand > PP soils (Table 2). Soils of K, V, and Touhaku types gave the highest values for point 1 and 2. The starting point for V, Touhaku and Sand soils is 0.8 and 1.6 for K soil. Whereas, Pearlite and PP soils got 0.3. From table 2 and within evapotranspiration ratio, it can be seen that K, V and Touhaku soils had almost similar values for point 1 and 2. Whereas, Sand, Pearlite and PP soils got the lowest values for transpiration. This reflects the poor structure of the soils and disability of the soil to hold water. It is also mean that soil was losing much water in short time and plant got stressed within short period. Since different soil has different properties of sand, silt and clay so each one was storing different amount of water and that

Sedum evapotranspiration ratio showed same results as found by many researchers [9, 10]. However, using different soil with different properties will give different values for point 1

> K soil 3.1 4.6 3.0 4.2 V soil 2.2 3.2 3.0 4.2 Sand 1.2 1.5 2.2 4.2 Touhaku 2.6 4.7 3.0 4.2 Pearlite 2.0 2.7 - - PP 0.8 1.3 - -

**T/E ET/E Point 1 Point 2 Point 1 Point 2**

between dotes and plotted line using equation 2.

was reflected in plant growth.

**Table 2.** The pF value of point 1and 2

and 2 (Table 2).

**Figure 7.** Relationship between cumulative transpiration ratio and square root elapse time

#### *Transpiration ratio and soil water potential*

Figure 8 shows soil water potential with transpiration ratio. The transpiring ratio for the study period decreased gradually with the increase in soil water potential (pF). The dotes shown in Figure 8 are the observation points. Whereas, the line was the predicted values found by equation 1.

$$\mathbf{y} = \alpha \left< \mathbf{l} + \boldsymbol{\beta}^\* \exp(-\boldsymbol{\gamma}^\* \mathbf{x}) \right> + \boldsymbol{\delta} \tag{1}$$

whereα, β, γ, and δ are fitting parameters. Root mean square error (RMSE) was calculated between dotes and plotted line using equation 2.

$$RMSE = \sqrt{\frac{\sum\_{i=1}^{n} d\_i^2}{N}} \tag{2}$$

where d is the difference between observed and calculated values and N is the total number of the data. The average value for RMSE is 0.0097 which mean there is a good fit between observed and calculated data. It can be seen that K and V soils were giving different graphs depending on physicochemical properties of each soil. Point 1 and point 2 are the changing points. A decrease of 10 % from highest point in the graph is a representation of point 1 and an increase by 10 % from lowest point is a representation for point 2. Many points were checked and 10 % of increase or decrease was giving the best data and matching with value of changing point. The best values for point 1 were found in K soil followed by Touhaku > V > Pearlite > Sand > PP soils. For point 2 the order is Touhaku > K > V > Pearlite > Sand > PP soils (Table 2). Soils of K, V, and Touhaku types gave the highest values for point 1 and 2. The starting point for V, Touhaku and Sand soils is 0.8 and 1.6 for K soil. Whereas, Pearlite and PP soils got 0.3. From table 2 and within evapotranspiration ratio, it can be seen that K, V and Touhaku soils had almost similar values for point 1 and 2. Whereas, Sand, Pearlite and PP soils got the lowest values for transpiration. This reflects the poor structure of the soils and disability of the soil to hold water. It is also mean that soil was losing much water in short time and plant got stressed within short period. Since different soil has different properties of sand, silt and clay so each one was storing different amount of water and that was reflected in plant growth.



**Table 2.** The pF value of point 1and 2

*Transpiration ratio assumption*

248 Evapotranspiration - An Overview

and Iijima [10].

In case of water stress, evapotranspiration could be a good indicator for plant survival. In this study cumulative transpiration and ET were related to square roots of elapse time (Fig‐ ure 7). Both studies in glasshouse and growth chamber were agreed with starting point but with the time, each study gave different patterns especially in the last days of measure‐ ments. This can be related to the environmental conditions of both studies. Glasshouse con‐ ditions were varied and both evaporation and transpiration were counted. In same time plant was growing under normal condition without any heat or drought stresses. Whereas, in growth chamber, the growth conditions were almost constant and transpiration was the main factor that was measured. In addition plant was growing under stress condition in which transpiration was decreasing with time. However, all values in growth chamber were highly correlated with R2 value of 0.99. This finding was also confirmed by Moritaniet al. [9]

**Figure 7.** Relationship between cumulative transpiration ratio and square root elapse time

Figure 8 shows soil water potential with transpiration ratio. The transpiring ratio for the study period decreased gradually with the increase in soil water potential (pF). The dotes shown in Figure 8 are the observation points. Whereas, the line was the predicted values

> g

 d

/{1 \*exp( \* )} (1)

*y x* =+ - +

ab

*Transpiration ratio and soil water potential*

found by equation 1.

of evapotranspiration as compared to saline water treatments (Figure 10). In general the higher level of evapotranspiration and accumulation of salts on the soil surface was caused

Evapotranspiration of Succulent Plant *(Sedum aizoonvar.floibundum)*

http://dx.doi.org/10.5772/53213

251

by the variations in the temperature over time.

**Figure 9.** Variations in temperature and humidity during study period

**Figure 10.** Variability in the evapotranspiration as affected by saline treatments

Fresh water encouraged evaporation process more than saline water. Maximum evapotrans‐ piration occurred with good quality water. Since the plants absorb water in saline conditions with higher pressure therefore the water losses through transpiration were retarded. Thus the magnitude of the evapotranspiration was inversely related to the amount of salts in the irrigation water. Reduced bioavailability of water and retarded plant growth under saline irrigation produced poor evapotranspiration in the system. On the other hand presence of salts in the saline irrigation inhibits evapotranspiration and reduces water consumption. Water density, viscosity and formation of salt crust are factors that could reduce evapora‐ tion and maintain higher water in the soils. Al-Busaidi and Cookson [15] reported salt crust formation on the soil surface due to saline irrigation inhibited evaporation and reduced

**Figure 8.** Relationship between transpiration ratio, evapotranspiration ratio and water potential

#### *Salinity study*

During the experiment, weather fluctuated with the average glasshouse temperature of 29 o C and humidity of 74 %. Changes in the temperature and humidity during the experiment are shown in Figure 9. Under fresh water treatment the plants exhibited the highest values of evapotranspiration as compared to saline water treatments (Figure 10). In general the higher level of evapotranspiration and accumulation of salts on the soil surface was caused by the variations in the temperature over time.

**Figure 9.** Variations in temperature and humidity during study period

**Figure 10.** Variability in the evapotranspiration as affected by saline treatments

**Figure 8.** Relationship between transpiration ratio, evapotranspiration ratio and water potential

During the experiment, weather fluctuated with the average glasshouse temperature of 29

C and humidity of 74 %. Changes in the temperature and humidity during the experiment are shown in Figure 9. Under fresh water treatment the plants exhibited the highest values

*Salinity study*

250 Evapotranspiration - An Overview

o

Fresh water encouraged evaporation process more than saline water. Maximum evapotrans‐ piration occurred with good quality water. Since the plants absorb water in saline conditions with higher pressure therefore the water losses through transpiration were retarded. Thus the magnitude of the evapotranspiration was inversely related to the amount of salts in the irrigation water. Reduced bioavailability of water and retarded plant growth under saline irrigation produced poor evapotranspiration in the system. On the other hand presence of salts in the saline irrigation inhibits evapotranspiration and reduces water consumption. Water density, viscosity and formation of salt crust are factors that could reduce evapora‐ tion and maintain higher water in the soils. Al-Busaidi and Cookson [15] reported salt crust formation on the soil surface due to saline irrigation inhibited evaporation and reduced leaching efficiency. It has been reported elsewhere that salt accumulation in root zone caus‐ es the development of osmotic stress and reduces plant development [16, 17].

holding capacity and composition of the salts. Abu-Awwad [20] reported that saline soils with considerable soluble salts interfered the growth of crop species. Heakal et al. [16] re‐ ported that dry matter yield of plants decreased with increasing salinity of irrigation water.

> **Fresh weight (g)**

Evapotranspiration of Succulent Plant *(Sedum aizoonvar.floibundum)*

**Dry weight (g)**

http://dx.doi.org/10.5772/53213

253

**Leaf area (cm2)**

0.7 (N) 31 11 355 44 0.7 (S) 25 10 314 39 15 (N) 20 5 69 22 15 (S) 20 4 57 16 30 (N) 17 3 39 17 30 (S) 16 3 43 18 46 (N) 14 2 42 17 46 (S) 14 2 35 20

In general the plant biomass is dependent absolutely on the growth of plants. Differences were found in the fresh and dry weights among the irrigation treatments. Water deficit level increased with the increasing salinity (Figure12). The ratio of dry weight to fresh plant weight increased significantly with the increasing level of salinity treatments. The stress caused by the ion concentrations allows the water gradient to decrease, making it more diffi‐ cult for water and nutrients to move through the root membrane [22]. Accumulation of salts in the root zone affects plant performance through creation of water deficit and disruption of ion homeostasis [23] which in turn cause metabolic dysfunctions. The differences in the water content of the plants between the irrigation methods could reflect the efficiency of sur‐ face irrigation which can provide enough water to the plant without physically touching the leaves. Sprinkler or shower irrigation adds salts directly on the leaves and may disturb its

**Figure 12.** The ratio of dry to fresh weight and water deficit (WD) as affected by the saline treatments

**Treatment Plant height**

normal functions.

**(cm)**

**Table 3.** Plant parameters as affected by saline water irrigation

Application of irrigation water with certain level of salts results the deposition of soluble salts in the soils. Evaporation and transpiration of irrigation water eventually accumulate excessive amounts of salts in the soils unless an adequate leaching and drainage systems are not practiced [18]. During the study, a low electrical conductivity of soil was noted under normal water whereas sea water irrigation largely increased the salinity level of soil (Figure 11). The saline water accumulated salts in the soil in spite of the leaching process. Petersen [19] reported that the accumulation and release of salts could depend on the quality and quantity of irrigation water, soil type and plant response. Abu-Awwad [20] reported high salt concentration on the soil surface due to evaporation.

**Figure 11.** Soil salinity under different saline irrigation treatments

### *Plant growth*

Plant parameters were the function of irrigation water treatments. Sedum plant grew well under non-saline conditions. Highest plant fresh and dry biomass, plant height and leaf area were noticed with normal irrigation water. While, sea water treatment gave the lowest val‐ ues of the plant parameters (Table 3). Soil salinity was the main reason behind the lower plant growth whereas the effects of irrigation methods were statistically found insignificant. Sedum plants accumulated more salts and leaf injuries were seen especially under high sal‐ ine treatments. The physiological thickness of the Sedum leaves with higher water absorb‐ ing potential could possibly facilitate Sedum plants to survive under high saline conditions. Usually, CAM plants are capable of transporting water very effectively to those tissues nec‐ essary for survival. This also happened in Sedum when the plants were dry, water was transported from the older leaflets to the younger parts of the shoots, which were thus kept turgescent, whereas the older leaflets died. Closure of the stomata helped further to main‐ tain a sufficiently high water potential [21].

There is a general consensus that higher salinity profoundly impaired plant growth parame‐ ters. The response of crops to salinity could depend upon plant species, soil texture, water


holding capacity and composition of the salts. Abu-Awwad [20] reported that saline soils with considerable soluble salts interfered the growth of crop species. Heakal et al. [16] re‐ ported that dry matter yield of plants decreased with increasing salinity of irrigation water.

**Table 3.** Plant parameters as affected by saline water irrigation

leaching efficiency. It has been reported elsewhere that salt accumulation in root zone caus‐

Application of irrigation water with certain level of salts results the deposition of soluble salts in the soils. Evaporation and transpiration of irrigation water eventually accumulate excessive amounts of salts in the soils unless an adequate leaching and drainage systems are not practiced [18]. During the study, a low electrical conductivity of soil was noted under normal water whereas sea water irrigation largely increased the salinity level of soil (Figure 11). The saline water accumulated salts in the soil in spite of the leaching process. Petersen [19] reported that the accumulation and release of salts could depend on the quality and quantity of irrigation water, soil type and plant response. Abu-Awwad [20] reported high

Plant parameters were the function of irrigation water treatments. Sedum plant grew well under non-saline conditions. Highest plant fresh and dry biomass, plant height and leaf area were noticed with normal irrigation water. While, sea water treatment gave the lowest val‐ ues of the plant parameters (Table 3). Soil salinity was the main reason behind the lower plant growth whereas the effects of irrigation methods were statistically found insignificant. Sedum plants accumulated more salts and leaf injuries were seen especially under high sal‐ ine treatments. The physiological thickness of the Sedum leaves with higher water absorb‐ ing potential could possibly facilitate Sedum plants to survive under high saline conditions. Usually, CAM plants are capable of transporting water very effectively to those tissues nec‐ essary for survival. This also happened in Sedum when the plants were dry, water was transported from the older leaflets to the younger parts of the shoots, which were thus kept turgescent, whereas the older leaflets died. Closure of the stomata helped further to main‐

There is a general consensus that higher salinity profoundly impaired plant growth parame‐ ters. The response of crops to salinity could depend upon plant species, soil texture, water

es the development of osmotic stress and reduces plant development [16, 17].

salt concentration on the soil surface due to evaporation.

**Figure 11.** Soil salinity under different saline irrigation treatments

tain a sufficiently high water potential [21].

*Plant growth*

252 Evapotranspiration - An Overview

In general the plant biomass is dependent absolutely on the growth of plants. Differences were found in the fresh and dry weights among the irrigation treatments. Water deficit level increased with the increasing salinity (Figure12). The ratio of dry weight to fresh plant weight increased significantly with the increasing level of salinity treatments. The stress caused by the ion concentrations allows the water gradient to decrease, making it more diffi‐ cult for water and nutrients to move through the root membrane [22]. Accumulation of salts in the root zone affects plant performance through creation of water deficit and disruption of ion homeostasis [23] which in turn cause metabolic dysfunctions. The differences in the water content of the plants between the irrigation methods could reflect the efficiency of sur‐ face irrigation which can provide enough water to the plant without physically touching the leaves. Sprinkler or shower irrigation adds salts directly on the leaves and may disturb its normal functions.

**Figure 12.** The ratio of dry to fresh weight and water deficit (WD) as affected by the saline treatments

Water salinity and irrigation method can affect plant growth. Moreover, the interaction ef‐ fect of both independent parameters was affecting plant height and biomass (Table 4). How‐ ever, it can be seen that all dependent parameters were significantly affected by applied treatments. Volkmar et al. [22] reported that plants grown in saline soils have diverse ionic compositions and concentrations of salts. The fluctuations in the salts concentrations could be related to the changes in the water source, drainage, evapotranspiration, and solute availabil‐ ity. The two major environmental factors that currently reduce plant productivity are drought and salinity and these stresses cause similar reactions in plants due to water stress [24].

transpiring ratio at the day and night was almost equal. However, transpiration value can be predicted from the relationship of the square root time and measured values for plant transpiration. Low transpiration values in the day time were related to the photosynthesis characteristic of Sedum with leaf water potential. In the night time where low temperature was observed, the stomata was open and plant was exchanging CO2 with more transpiration rate compared to the day time. In salinity study, the experiment could confirm that Sedum plants can tolerate salinity stress and can survive with water deficit conditions, which was related to its ability to store water for long time. However, the saline waters remarkably af‐ fected the evapotranspiration rate, salts accumulation in the soils and plant biomass produc‐ tion. Water deficit increased with the increase in salinity level. The salinity of the soil significantly increased with higher saline water. The plant growth was not affected by sur‐ face or sprinkler irrigation methods. The use of sea water up to certain dilution could be an

Evapotranspiration of Succulent Plant *(Sedum aizoonvar.floibundum)*

http://dx.doi.org/10.5772/53213

255

and S. Moritani2

1 College of Agricultural & Marine Sciences, Department of Soils, Water and Agricultural

[1] Stephenson, R. (1994). Sedum Cultivated Stonecrops. *Timber press, Inc., Oregon, USA.*

[2] Berghage, R., Beattie, D., Jarrett, A., & Rezaei, F. (2007). Green Roof Plant Water Use. *BerghageR., et al. Quantifying Evaporation and Transpirational Water Losses from Green Roofs and Green Roof Media Capacity for Neutralizing Acid Rain.The Pennsylvania State*

[3] Durhman, A. K., Rowe, D. B., & Rugh, C. L. (2007). Effect of Substrate Depth on Ini‐ tial Growth, Coverage, and Survival of 25 Succulent Green Roof Plant Taxa. *HortS‐*

[4] Latocha, P., & Batorska, A. (2007). The Influence of Irrigation System on Growth Rate and Frost Resistance of Chosen Ground Cover Plants on Extensive Green Roofs. *An‐ nals of Warsaw University of Life Sciences-SGGW.Horticulture and Landscape Architec‐*

*ture.Warsaw University of Life Sciences Press, Warsaw, Poland*, 131-137.

option for Sedum production in water scarce areas.

Engineering, Sultan Qaboos University, Oman

*University, State College, PA.*, 18-38.

*cience*, 42, 588-595.

2 Arid Land Research Center, Tottori University, Japan

, S. Tanak2

\*Address all correspondence to: albusaidiahmed@yahoo.com

**Author details**

**References**

A. Al-Busaidi1\*, T. Yamamoto2


**Table 4.** Summary of two-way analysis of variance on the effects of saline water and irrigation method on plant parameters\* denotes the level of significance at P value < 0.05 and NS denotes non-significance.

Most studies of CAM plants have focused on the physiology and ecology of individual plant performance. It has generally been assumed that the expression of CAM is associated with adaptive success in arid environments because traits related to water use efficiency and tolerance of low water availability are genetically correlated with CAM. Water loss in CAM plants is reduced as a result of low stomatal frequency and high cuticular resistance [11, 25-27].

It is known that malate accumulation in at least some CAM plants can result in a substantial level of osmotic adjustment [28]. The maintenance of negative leaf potential during drought appears to be related to the continued ability of the Amistad plants to take up CO2 and to accumulate dry weight. Both Troughton et al. [29] and Mooney et al. [30] have found that reproductive tissue in a variety of leaf succulents may have carbon isotope ratios that are considerably less negative than those of vegetative tissue from the same plant. While this may relate to the concurrence of drought and reproduction, it does illustrate that CAM ac‐ tivity may make an important contribution to reproductive carbon sinks.

### **4. Conclusion**

All plants are subjected to a multitude of stresses throughout their life cycle. Depending on the plant species and stress source, the plant will respond in different ways. Sedum is a drought tolerant plant. Its ability to grow with different soil types and under water stress condition was investigated. The main reason for the difference in water loss between treat‐ ments was differences in soil types. At the end of growth chamber study, it was found that transpiring ratio at the day and night was almost equal. However, transpiration value can be predicted from the relationship of the square root time and measured values for plant transpiration. Low transpiration values in the day time were related to the photosynthesis characteristic of Sedum with leaf water potential. In the night time where low temperature was observed, the stomata was open and plant was exchanging CO2 with more transpiration rate compared to the day time. In salinity study, the experiment could confirm that Sedum plants can tolerate salinity stress and can survive with water deficit conditions, which was related to its ability to store water for long time. However, the saline waters remarkably af‐ fected the evapotranspiration rate, salts accumulation in the soils and plant biomass produc‐ tion. Water deficit increased with the increase in salinity level. The salinity of the soil significantly increased with higher saline water. The plant growth was not affected by sur‐ face or sprinkler irrigation methods. The use of sea water up to certain dilution could be an option for Sedum production in water scarce areas.

### **Author details**

Water salinity and irrigation method can affect plant growth. Moreover, the interaction ef‐ fect of both independent parameters was affecting plant height and biomass (Table 4). How‐ ever, it can be seen that all dependent parameters were significantly affected by applied treatments. Volkmar et al. [22] reported that plants grown in saline soils have diverse ionic compositions and concentrations of salts. The fluctuations in the salts concentrations could be related to the changes in the water source, drainage, evapotranspiration, and solute availabil‐ ity. The two major environmental factors that currently reduce plant productivity are drought and salinity and these stresses cause similar reactions in plants due to water stress [24].

**Parameter Saline water (S) Irrigation method (I) S x I**

Plant height 0.0001\* 0.0001\* 0.0002\* Leaf area 0.0001\* NS NS Fresh weight 0.0001\* 0.0001\* 0.0001\* Dry weight 0.0001\* 0.0006\* 0.0001\*

**Table 4.** Summary of two-way analysis of variance on the effects of saline water and irrigation method on plant

Most studies of CAM plants have focused on the physiology and ecology of individual plant performance. It has generally been assumed that the expression of CAM is associated with adaptive success in arid environments because traits related to water use efficiency and tolerance of low water availability are genetically correlated with CAM. Water loss in CAM plants is reduced as a result of low stomatal frequency and high cuticular resistance [11, 25-27].

It is known that malate accumulation in at least some CAM plants can result in a substantial level of osmotic adjustment [28]. The maintenance of negative leaf potential during drought appears to be related to the continued ability of the Amistad plants to take up CO2 and to accumulate dry weight. Both Troughton et al. [29] and Mooney et al. [30] have found that reproductive tissue in a variety of leaf succulents may have carbon isotope ratios that are considerably less negative than those of vegetative tissue from the same plant. While this may relate to the concurrence of drought and reproduction, it does illustrate that CAM ac‐

All plants are subjected to a multitude of stresses throughout their life cycle. Depending on the plant species and stress source, the plant will respond in different ways. Sedum is a drought tolerant plant. Its ability to grow with different soil types and under water stress condition was investigated. The main reason for the difference in water loss between treat‐ ments was differences in soil types. At the end of growth chamber study, it was found that

parameters\* denotes the level of significance at P value < 0.05 and NS denotes non-significance.

tivity may make an important contribution to reproductive carbon sinks.

**4. Conclusion**

254 Evapotranspiration - An Overview

P-value


1 College of Agricultural & Marine Sciences, Department of Soils, Water and Agricultural Engineering, Sultan Qaboos University, Oman

2 Arid Land Research Center, Tottori University, Japan

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**Chapter 13**

**Reference Evapotranspiration (ETo) in North**

**of Analysis**

José Carlos Mendonça,

Elias Fernandes de Sousa

http://dx.doi.org/10.5772/52278

**1. Introduction**

Barbara dos Santos Esteves and

Additional information is available at the end of the chapter

ing or other applications (Ferreira et al., 2011.)

**Fluminense, Rio de Janeiro, Brazil: A Review of**

**Methodologies of the Calibration for Different Periods**

Water is the essential element for life on Earth planet, where currently different regions suf‐ fer from shortages due to the large population growth and depletion of natural sources. The agricultural sector is the human activity that consumes the most water in the world (about 70% of drinking water sources) and one of the main problems of irrigated agriculture is the correct quantification of crop water requirements. In this sense, there is a constant search to implement sustainable practices for the management of water resources, one of the more ef‐ ficient determination of evapotranspiration (ET), which is the term used to describe the amount of water effectively ceded the land surface to atmosphere and an important compo‐ nent of the hydrological cycle and used for quantifying the calculation of water balance in soil, detection of water stress conditions and use as input for quantitative models of harvest‐

With the objective to standardize the definition of evapotranspiration given by various authors, as Penman (1948) and Thornthwaite (1948), it became necessary to define the ref‐ erence evapotranspiration (ETo), which according to Allen et al. (1998) can be defined as the rate of evapotranspiration from a hypothetical crop with an assumed height of 0.12 m, with a surface resistance of 70 sec/m and an albedo of 0.23, closely resembling the evapo‐

> © 2013 Mendonça et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Mendonça et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the Calibration for Different Periods of Analysis**

José Carlos Mendonça, Barbara dos Santos Esteves and Elias Fernandes de Sousa

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/52278

**1. Introduction**

Water is the essential element for life on Earth planet, where currently different regions suf‐ fer from shortages due to the large population growth and depletion of natural sources. The agricultural sector is the human activity that consumes the most water in the world (about 70% of drinking water sources) and one of the main problems of irrigated agriculture is the correct quantification of crop water requirements. In this sense, there is a constant search to implement sustainable practices for the management of water resources, one of the more ef‐ ficient determination of evapotranspiration (ET), which is the term used to describe the amount of water effectively ceded the land surface to atmosphere and an important compo‐ nent of the hydrological cycle and used for quantifying the calculation of water balance in soil, detection of water stress conditions and use as input for quantitative models of harvest‐ ing or other applications (Ferreira et al., 2011.)

With the objective to standardize the definition of evapotranspiration given by various authors, as Penman (1948) and Thornthwaite (1948), it became necessary to define the ref‐ erence evapotranspiration (ETo), which according to Allen et al. (1998) can be defined as the rate of evapotranspiration from a hypothetical crop with an assumed height of 0.12 m, with a surface resistance of 70 sec/m and an albedo of 0.23, closely resembling the evapo‐

© 2013 Mendonça et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Mendonça et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ration from an extensive surface of green grass of uniform height, actively growing and adequately watered.

different weather conditions and location is recommended by the FAO, the lack of lysime‐

Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the…

http://dx.doi.org/10.5772/52278

261

Zanetti et al. (2007) tested an artificial neural network (ANN) for estimating the reference evepotranspiration (ETo) as a function of the maximum and minimum air temperatures in the Campos dos Goytacazes, Rio de Janeiro State. The data used in the network training were obtained from a historical series (September 1996 to August 2002) of daily climatic data collected in Campos dos Goytacazes. When testing the artificial neural network, two histori‐ cal series were used (September 2002 to August 2003) relative to Campos dos Goytacazes, Rio de Janeiro and Viçosa, Minas Gerais State. The ANNs (multilayer perceptron type) were trained to estimate ETo as a function of the maximum and minimum air temperatures, ex‐ traterrestrial radiation, and the daylight hours; and the last two were previously calculated as a function of either the local latitude or the Julian date. According to the results obtained in this ANN testing phase, it is concluded that when taking into account just the maximum and minimum air temperatures, it is possible to estimate ETo in Campos dos Goytacazes, RJ. One work was performed with the aim of proposing an artificial neural network (ANN) to estimate the reference evapotranspiration (ETo) as a function of geographic position coordi‐ nates and air temperature in the State of Rio de Janeiro (Zanetti et al., 2008). Data used for the network training were collected from 17 historical time series of climatic elements locat‐ ed in the State of Rio de Janeiro. The daily ETo calculated by Penman-Monteith (FAO-56) method was used as a reference for network training. ANNs of multilayer perceptron type were trained to estimate ETo as a function of latitude, longitude, altitude, mean air tempera‐ ture, thermal daily amplitude and day of the year. After training with different network configurations, the one showing best performance was selected, and was composed by only one intermediary layer (with twenty neurons and sigmoid logistic activation function) and one output layer (with one neuron and linear activation function). According to the results obtained it can be concluded that, considering only geographical positioning coordinates and air temperature, it is possible to estimate daily ETo in 17 places of Rio de Janeiro State

Another method of estimating the ETo are evaporimeters, which measure the evaporation of water, the most common Class "A" Pan developed by the U.S. Weather Service (USWB) and widespread use. According to Pereira et al. (1997) Class "A" Pan (TCA) is influenced by solar radiation, wind speed, temperature and relative humidity and thus, different researchers have questioned the methodology of choice of the pan coefficient (Kt) and should be deter‐

It is observed that the choice of methodology to be adopted should be based on the availa‐ bility of climate data, the necessary precision, convenience and cost. In irrigation projects are required for short periods, ranging from daily to a maximum of fortnightly research is need‐ ed to evaluate the efficiency of the methodologies in these conditions. Using a series of ten years of daily average data collected at Evapotranspirometric Station of Universidade Estad‐ ual do Norte Fluminense Darcy Ribeiro, this study aimed to evaluate the performance of in‐ direct methods for estimating reference evapotranspiration (ETo) proposed by Hargreaves-Samani (1985), FAO-24 Radiation Solar (1977), Jensen-Haise (1963), Linacre (1977), Makkink

mined by results of scientific research estimates that there are no wrong.

ters as calibration standard in the world.

by using an ANN.

Several researchers have developed methods for estimating and measuring evapotranspi‐ ration. Burman et al. (1983) did a review of these methods in different parts of the world and commented that many methods have been proposed and the methods may be broad‐ ly classified as those based on combination theory, humidity data, radiation data, temper‐ ature data, and miscellaneous methods which usually involve multiple correlations of ET and various climate data. Usually the reference evapotranspiration methods are classified in Combination methods, Radiation method, Temperature methods, pan evapotranspira‐ tion, etc.

Allen et al. (1998) mentioning that evapotranspiration is not easy to measure. Specific de‐ vices and accurate measurements of various physical parameters or the soil water bal‐ ance in lysimeters are required to determine evapotranspiration. The methods are often expensive, demanding in terms of accuracy of measurement and can only be fully exploit‐ ed by well-trained research personnel. Although the methods are inappropriate for rou‐ tine measurements, they remain important for the evaluation of ET estimates obtained by more indirect methods.

Since the 1930s there are several methods for estimating ETo. However, whatever the meth‐ od is detailed and rigorous, there will always be the needs of local or regional calibrations if you are being adopted outside the region where it was developed. Burman et al (1983) argue that several equations to estimate reference evapotranspiration developed around the world use the grass and alfalfa as a standard surface. This situation creates difficulties as the pro‐ posal for an empirical equation bears a strong dependence on the standard surface, causing undesirable and significant errors in estimation. Based on these discussions is that the Pen‐ man-Monteith equation was parameterized by Allen et al. (1998).

The surface resistance is defined as the resistance of water vapor through the openings of stomata and drag as that of the upper plant, involving the friction of the air flow over the surface vegetated. The aerodynamic resistance is a parameter dependent on the local weath‐ er and its demonstration of layers depends on the roughness governing the processes of transport of momentum and heat, and the offset and zero plane. This displacement of the zero plane refers to the height to which the speed is zero. Thereafter the profile starts log wind speed. However, the aerodynamic resistance scheme used in the formulation Penman-Monteith (FAO, 56) is restricted to the condition parameter neutral atmosphere, ie when the air temperature, atmospheric pressure and wind speed field close to the adiabatic condition. One can also be noted that the displacement of the zero plane and the layers of roughness, the processes that govern the amount of heat transport is correlated with the height of cul‐ ture and as regards the parameter of surface resistance, it is directly proportional stomatal resistance and inversely proportional to the active leaf area index, stomatal resistance being directly affected by atmospheric conditions and the availability of water for the crop.

Allen et al. (1998) clain that the Penman-Monteith(FAO-56) for estimating reference evapo‐ transpiration does not allow controversy and provides consistent and reliable information in different weather conditions and location is recommended by the FAO, the lack of lysime‐ ters as calibration standard in the world.

ration from an extensive surface of green grass of uniform height, actively growing and

Several researchers have developed methods for estimating and measuring evapotranspi‐ ration. Burman et al. (1983) did a review of these methods in different parts of the world and commented that many methods have been proposed and the methods may be broad‐ ly classified as those based on combination theory, humidity data, radiation data, temper‐ ature data, and miscellaneous methods which usually involve multiple correlations of ET and various climate data. Usually the reference evapotranspiration methods are classified in Combination methods, Radiation method, Temperature methods, pan evapotranspira‐

Allen et al. (1998) mentioning that evapotranspiration is not easy to measure. Specific de‐ vices and accurate measurements of various physical parameters or the soil water bal‐ ance in lysimeters are required to determine evapotranspiration. The methods are often expensive, demanding in terms of accuracy of measurement and can only be fully exploit‐ ed by well-trained research personnel. Although the methods are inappropriate for rou‐ tine measurements, they remain important for the evaluation of ET estimates obtained by

Since the 1930s there are several methods for estimating ETo. However, whatever the meth‐ od is detailed and rigorous, there will always be the needs of local or regional calibrations if you are being adopted outside the region where it was developed. Burman et al (1983) argue that several equations to estimate reference evapotranspiration developed around the world use the grass and alfalfa as a standard surface. This situation creates difficulties as the pro‐ posal for an empirical equation bears a strong dependence on the standard surface, causing undesirable and significant errors in estimation. Based on these discussions is that the Pen‐

The surface resistance is defined as the resistance of water vapor through the openings of stomata and drag as that of the upper plant, involving the friction of the air flow over the surface vegetated. The aerodynamic resistance is a parameter dependent on the local weath‐ er and its demonstration of layers depends on the roughness governing the processes of transport of momentum and heat, and the offset and zero plane. This displacement of the zero plane refers to the height to which the speed is zero. Thereafter the profile starts log wind speed. However, the aerodynamic resistance scheme used in the formulation Penman-Monteith (FAO, 56) is restricted to the condition parameter neutral atmosphere, ie when the air temperature, atmospheric pressure and wind speed field close to the adiabatic condition. One can also be noted that the displacement of the zero plane and the layers of roughness, the processes that govern the amount of heat transport is correlated with the height of cul‐ ture and as regards the parameter of surface resistance, it is directly proportional stomatal resistance and inversely proportional to the active leaf area index, stomatal resistance being

directly affected by atmospheric conditions and the availability of water for the crop.

Allen et al. (1998) clain that the Penman-Monteith(FAO-56) for estimating reference evapo‐ transpiration does not allow controversy and provides consistent and reliable information in

man-Monteith equation was parameterized by Allen et al. (1998).

adequately watered.

260 Evapotranspiration - An Overview

more indirect methods.

tion, etc.

Zanetti et al. (2007) tested an artificial neural network (ANN) for estimating the reference evepotranspiration (ETo) as a function of the maximum and minimum air temperatures in the Campos dos Goytacazes, Rio de Janeiro State. The data used in the network training were obtained from a historical series (September 1996 to August 2002) of daily climatic data collected in Campos dos Goytacazes. When testing the artificial neural network, two histori‐ cal series were used (September 2002 to August 2003) relative to Campos dos Goytacazes, Rio de Janeiro and Viçosa, Minas Gerais State. The ANNs (multilayer perceptron type) were trained to estimate ETo as a function of the maximum and minimum air temperatures, ex‐ traterrestrial radiation, and the daylight hours; and the last two were previously calculated as a function of either the local latitude or the Julian date. According to the results obtained in this ANN testing phase, it is concluded that when taking into account just the maximum and minimum air temperatures, it is possible to estimate ETo in Campos dos Goytacazes, RJ.

One work was performed with the aim of proposing an artificial neural network (ANN) to estimate the reference evapotranspiration (ETo) as a function of geographic position coordi‐ nates and air temperature in the State of Rio de Janeiro (Zanetti et al., 2008). Data used for the network training were collected from 17 historical time series of climatic elements locat‐ ed in the State of Rio de Janeiro. The daily ETo calculated by Penman-Monteith (FAO-56) method was used as a reference for network training. ANNs of multilayer perceptron type were trained to estimate ETo as a function of latitude, longitude, altitude, mean air tempera‐ ture, thermal daily amplitude and day of the year. After training with different network configurations, the one showing best performance was selected, and was composed by only one intermediary layer (with twenty neurons and sigmoid logistic activation function) and one output layer (with one neuron and linear activation function). According to the results obtained it can be concluded that, considering only geographical positioning coordinates and air temperature, it is possible to estimate daily ETo in 17 places of Rio de Janeiro State by using an ANN.

Another method of estimating the ETo are evaporimeters, which measure the evaporation of water, the most common Class "A" Pan developed by the U.S. Weather Service (USWB) and widespread use. According to Pereira et al. (1997) Class "A" Pan (TCA) is influenced by solar radiation, wind speed, temperature and relative humidity and thus, different researchers have questioned the methodology of choice of the pan coefficient (Kt) and should be deter‐ mined by results of scientific research estimates that there are no wrong.

It is observed that the choice of methodology to be adopted should be based on the availa‐ bility of climate data, the necessary precision, convenience and cost. In irrigation projects are required for short periods, ranging from daily to a maximum of fortnightly research is need‐ ed to evaluate the efficiency of the methodologies in these conditions. Using a series of ten years of daily average data collected at Evapotranspirometric Station of Universidade Estad‐ ual do Norte Fluminense Darcy Ribeiro, this study aimed to evaluate the performance of in‐ direct methods for estimating reference evapotranspiration (ETo) proposed by Hargreaves-Samani (1985), FAO-24 Radiation Solar (1977), Jensen-Haise (1963), Linacre (1977), Makkink (1957), Penman Simplified (2006) and Pan Class "A" estimated using four equations for de‐ termining the coefficient of the Pan - Kt: Allen (1998), Bernardo et al. (1996), Cuenca (1989) and Snyder (1992) for periods of 1, 5 and 10 days, with the Penman-Monteith FAO-parame‐ terized, in the North Fluminense, Rio de Janeiro, Brazil.

**•** Global Solar Radiation: A pyranometer can measure values in the range 0 to 1400 W/m2;

Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the…

All sensors are connected to a datalogger model DL-15 - V. 2:00 – Thies Clima, with total capacity of 256 Kbytes of memory storage, recording daily averages between 24-h. The sen‐

Observations the conventional meteorological station (Class A pan and weighing lysimeter)

The lysimeter tank with dimensions of 3.0 x 2.0 x 1.5 m, made of sheet metal had their weight carried by a set of four load cells manufactured by J-Star Electronics, Wisconsin, and installed at the tank base, and determining the lysimeter blade evapotranspired obtained by variation in weight observed in the period divided by evaporating surface area (6 m2).The

The Penman-Monteith parameterized by Allen et al.(1998) was selected as a benchmark

<sup>900</sup> 0,408 Rn G ue e

g

D -+ - <sup>+</sup> <sup>=</sup> D+ +

g

( ) ( ) ( )

1 0,34u

2

2s a

(1)

http://dx.doi.org/10.5772/52278

263

**•** Precipitation: A rain gauge measuring rainfall intensity of up to 7 mm/min.

sor values recorded every minute, and a stored mean value every 6 minutes

station area is covered with grass Batatais (Paspalum notatun Fluegge).

T 273 ETo

/day;

**2.2. Methods for obtaining the reference evapotranspiration (ETo)**

*2.2.1. FAO Penman-Monteith method (FAO-PM - 1998)*

method for comparation can be derived (Equation 1).

ETo is the reference evapotranspiration, in mm/day;

Rn - net radiation at crop surface, in MJ m-2/day;

G -soil heat flux density, in MJ/m2

*γ*- psychrometric constant, kPa/C;

T - air temperature at 2 m height, in °C;

Δ -slope vapor pressure curve, in kPa;

u2 - wind speed at 2 m height, in m/s;

es - saturation vapor pressure, in kPa;

es - ea-the saturation vapor pressure deficit, in kPa.

ea - actual vapor pressure, kPa;

for such work were performed at 9 h.

Where:

### **2. Materials and methods**

### **2.1. Study area**

The city of Campos dos Goytacazes located in the North Fluminense occupies an area of 4.027 km2 . The downtown area is located in the following geographical coordinates: 21o 45" 23' south latitude, 41o 19" 40' west longitude and 14 m above sea level. In Figure 1 is presented the study area contained in the North Fluminense, in reference to the state of Rio de Janeiro and Brazil. According Köeppen climate, this region's clime is classified as Aw, that is, tropical humid, with rainy summer, dry winter and the temperature average above 18°C during the coolest months. The annual average temperature stands at around 24 º C and the small temperature range; The climatological normal rainfall is 1055.3 mm (Ramos et al., 2009).

**Figure 1.** Study area localization in reference to the Rio de Janeiro State and Brazil.

In this study were used weather data daily, a period of 10 years (1996-2006), collected by an automatic station, model Thies Clima, installed at the Experimental Station of Pesagro-Rio (geographical coordinates: 21°18'47" south; 41º18'24'' west and altitude of 11 meters).

The Thies automatic weather station is equipped with sensors for measuring meteorological data the following:


All sensors are connected to a datalogger model DL-15 - V. 2:00 – Thies Clima, with total capacity of 256 Kbytes of memory storage, recording daily averages between 24-h. The sen‐ sor values recorded every minute, and a stored mean value every 6 minutes

Observations the conventional meteorological station (Class A pan and weighing lysimeter) for such work were performed at 9 h.

The lysimeter tank with dimensions of 3.0 x 2.0 x 1.5 m, made of sheet metal had their weight carried by a set of four load cells manufactured by J-Star Electronics, Wisconsin, and installed at the tank base, and determining the lysimeter blade evapotranspired obtained by variation in weight observed in the period divided by evaporating surface area (6 m2).The station area is covered with grass Batatais (Paspalum notatun Fluegge).

#### **2.2. Methods for obtaining the reference evapotranspiration (ETo)**

#### *2.2.1. FAO Penman-Monteith method (FAO-PM - 1998)*

The Penman-Monteith parameterized by Allen et al.(1998) was selected as a benchmark method for comparation can be derived (Equation 1).

$$\text{ETo} = \frac{0,408\,\text{A}\left(\text{Rn} - \text{G}\right) + \gamma \frac{900}{\text{T} + 273} \,\text{u}\_2\left(\text{e}\_s - \text{e}\_\text{a}\right)}{\Delta + \gamma \left(1 + 0,34\,\text{u}\_2\right)}\tag{1}$$

Where:

(1957), Penman Simplified (2006) and Pan Class "A" estimated using four equations for de‐ termining the coefficient of the Pan - Kt: Allen (1998), Bernardo et al. (1996), Cuenca (1989) and Snyder (1992) for periods of 1, 5 and 10 days, with the Penman-Monteith FAO-parame‐

The city of Campos dos Goytacazes located in the North Fluminense occupies an area of

45" 23' south latitude, 41o 19" 40' west longitude and 14 m above sea level. In Figure 1 is presented the study area contained in the North Fluminense, in reference to the state of Rio de Janeiro and Brazil. According Köeppen climate, this region's clime is classified as Aw, that is, tropical humid, with rainy summer, dry winter and the temperature average above 18°C during the coolest months. The annual average temperature stands at around 24 º C and the small temperature range; The climatological normal rainfall is 1055.3 mm

In this study were used weather data daily, a period of 10 years (1996-2006), collected by an automatic station, model Thies Clima, installed at the Experimental Station of Pesagro-Rio

The Thies automatic weather station is equipped with sensors for measuring meteorological

**•** Temperature and Relative Humidity: A thermo-hygrometer allows register values of rela‐

**•** Atmospheric Pressure: A barometer can measure values in the range 946 to 1053 hPa;

tive humidity in the range 1-100% and a temperature range of -35 to + 70 °C;

(geographical coordinates: 21°18'47" south; 41º18'24'' west and altitude of 11 meters).

**•** Wind Speed: a sensor to detect the wind speed in the range 0.3 to 50 m / s;

. The downtown area is located in the following geographical coordinates: 21o

terized, in the North Fluminense, Rio de Janeiro, Brazil.

**Figure 1.** Study area localization in reference to the Rio de Janeiro State and Brazil.

**2. Materials and methods**

**2.1. Study area**

262 Evapotranspiration - An Overview

(Ramos et al., 2009).

data the following:

4.027 km2

ETo is the reference evapotranspiration, in mm/day;

Rn - net radiation at crop surface, in MJ m-2/day;

G -soil heat flux density, in MJ/m2 /day;

T - air temperature at 2 m height, in °C;

*γ*- psychrometric constant, kPa/C;

Δ -slope vapor pressure curve, in kPa;

u2 - wind speed at 2 m height, in m/s;

es - saturation vapor pressure, in kPa;

ea - actual vapor pressure, kPa;

es - ea-the saturation vapor pressure deficit, in kPa.

*2.2.2. FAO – 24 Radiation method (1977)*

The estimate ETo by the FAO - 24 Radiation method was described for Doorenbos and Pruitt (1977) andcan be derived (equation 02)

$$ETo = c\_o + cL \text{ WRs} \tag{2}$$

*ETo Rs T* = + (0,0252 0,078) (6)

D + (7)

http://dx.doi.org/10.5772/52278

265

(8)

*2.2.5. Makkink method (1957)*

Δ -slope vapor pressure curve, in kPa/<sup>o</sup>

(Tdew) can be estimated by equation 09:

*2.2.7. Simplified Penman's Method (2006)*

*γ*- psychrometric constant, kPa/<sup>o</sup>

*2.2.6. Linacre method (1977)*

Where

For the estimation of ETo by the Makkink method used the equation 07:

*ETo Rs*( ) 0,12 g

Rs - Radiation at the surface, expressed as equivalent evaporation (Rs, mm/day);

C;

C.

For the estimation of ETo by the Linacre method used the equation 08:

100

Where ea is the vapor pressure of water in kPa, determined by equation 10:

Where RU (%) - relative humidity and es - saturation vapour pressure, inkPa/<sup>o</sup>

+

*ETo*

*dew*

*T*

D = +

Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the…

( ) ( ) 0,006 <sup>15</sup>

Where J is a dimensionless constant equal to 700; h is the local altitude in meters; ϕ is the local latitude degrees and To is the temperature of dew point. The dew point temperature

( )

*e*

A simplified estimation method to calculate the potential evapotranspiration was developed to Villa Nova et al. (2006) based on the Penman approach, considering only the diurnal val‐

237,3 log 156,8 8,16 log *a*

( )

*e*

*a*

*T*

*dew*


( ) 0,01 (%) *a s e e T RU* = (10)

C.

80

j

+ - - <sup>=</sup> -

*JT h T T*

Where

C0 =-0,3; a0 = 1,0656 ; a1 = -0,0012795 ; a2 = 0,044953 ; a3 = -0,00020033 ; a4 = -0,000031508 ; a5 = -0,0011026

cL =- a0 + a1 UR + a2 Vd + a3 UR Vd+ a4 UR2 + a5 Vd2

UR = Relative Humidity (%);

Vd = Average wind speed during the day to 2 m in height, in m/s (considered to Vd = 70% of the average wind speed within 24 h);

Rs - Radiation at the surface, expressed as equivalent evaporation (Rs, mm/day);

W - Weight factor dependent on the temperature (Tair).

The weighting factor (W) can be obtained by the following equations:

$$\dot{W} = 0.407 + 0.0145 T\_{air} \dot{f} \\ 0 < T\_{air} < 16^{\circ} \text{C} \tag{3}$$

$$\text{Cov} = 0, 483 + 0, 01T\_{air} \text{ if } 16, 1 < T\_{air} < 32^{\alpha} \text{ C} \tag{4}$$

Where Tu is the average daily temperature of air, to take Tu = Tar.

#### *2.2.3. Hargreaves –Samani method (1985)*

The Hargreaves - Samani method data requires only air temperature and extraterrestrial ra‐ diation to estimate ETo. For applicationused thefollowing equation:

$$ETo = 0,0023 \, Ra \left( Tm \dot{\alpha} x - T \min \right)^{0.5} \left( T + 17, 8 \right) \tag{5}$$

Where: Ra extraterrestrial radiation, in mm day-1, T max is the maximum temperature in °C;Tmin is the minimum temperature, in °C.

#### *2.2.4. Jansen-Haise method (1963)*

For the estimation of ETo by Jensen-Haise method used the equation 06:

Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the… http://dx.doi.org/10.5772/52278 265

$$ETo = Rs \left(0, 0252 \, T + 0, 078\right) \tag{6}$$

#### *2.2.5. Makkink method (1957)*

For the estimation of ETo by the Makkink method used the equation 07:

$$ETo = Rs\left(\frac{\Delta}{\Delta + \gamma}\right) + 0,12\tag{7}$$

Where

*2.2.2. FAO – 24 Radiation method (1977)*

264 Evapotranspiration - An Overview

Where

= -0,0011026

Pruitt (1977) andcan be derived (equation 02)

cL =- a0 + a1 UR + a2 Vd + a3 UR Vd+ a4 UR2

W - Weight factor dependent on the temperature (Tair).

UR = Relative Humidity (%);

the average wind speed within 24 h);

*2.2.3. Hargreaves –Samani method (1985)*

°C;Tmin is the minimum temperature, in °C.

*2.2.4. Jansen-Haise method (1963)*

The estimate ETo by the FAO - 24 Radiation method was described for Doorenbos and

C0 =-0,3; a0 = 1,0656 ; a1 = -0,0012795 ; a2 = 0,044953 ; a3 = -0,00020033 ; a4 = -0,000031508 ; a5

Vd = Average wind speed during the day to 2 m in height, in m/s (considered to Vd = 70% of

The Hargreaves - Samani method data requires only air temperature and extraterrestrial ra‐

Where: Ra extraterrestrial radiation, in mm day-1, T max is the maximum temperature in

Rs - Radiation at the surface, expressed as equivalent evaporation (Rs, mm/day);

The weighting factor (W) can be obtained by the following equations:

Where Tu is the average daily temperature of air, to take Tu = Tar.

diation to estimate ETo. For applicationused thefollowing equation:

For the estimation of ETo by Jensen-Haise method used the equation 06:

+ a5 Vd2

*<sup>o</sup> ETo c cL W Rs* = + (2)

0,407 0,0145 0 16º *W air air* = + << *T if T C* (3)

0,483 0,01 16,1 32º *W air air* = + << *T if T C* (4)

( ) ( ) 0,5 *ETo Ra Tmáx T T* = -+ 0,0023 min 17,8 (5)

Rs - Radiation at the surface, expressed as equivalent evaporation (Rs, mm/day);

Δ -slope vapor pressure curve, in kPa/<sup>o</sup> C; *γ*- psychrometric constant, kPa/<sup>o</sup> C.

*2.2.6. Linacre method (1977)*

For the estimation of ETo by the Linacre method used the equation 08:

$$T\_i = \frac{J\left(T + 0, 006\text{ }h\right)}{100 - \varphi} + 15\left(T - T\_{dew}\right)$$

$$80 - T$$

Where J is a dimensionless constant equal to 700; h is the local altitude in meters; ϕ is the local latitude degrees and To is the temperature of dew point. The dew point temperature (Tdew) can be estimated by equation 09:

$$T\_{dev} = \frac{237,3\log\left(e\_a\right) - 156,8}{8,16 - \log\left(e\_a\right)}\tag{9}$$

Where ea is the vapor pressure of water in kPa, determined by equation 10:

$$e\_a = e\_s(T)\,0,01\,RLl(\%)\tag{10}$$

Where RU (%) - relative humidity and es - saturation vapour pressure, inkPa/<sup>o</sup> C.

#### *2.2.7. Simplified Penman's Method (2006)*

A simplified estimation method to calculate the potential evapotranspiration was developed to Villa Nova et al. (2006) based on the Penman approach, considering only the diurnal val‐ ues of evapotranspiration rates thatare more representative of the water vapor transfer proc‐ ess to the atmosphere for a givenagricultural ecosystem. In addition, the classical expression of the Bowen ratio (b) was modifiedherein by considering the sensible heat flux (H) emer‐ gent from the evaporative surface inconjunction with the air turbulent flux, which trans‐ ports also latent heat flux (LE). Such procedureresults in a similarity between the aerodynamic resistances of sensible heat and latent heat fluxes soas to allow for a considera‐ ble simplification without impairing the estimates.

ETo estimated by the SPM proposed by Villa Nova et al. (2006) was obtained from equation 11:

$$ETo = 0,408 \ \frac{(Rn - G)}{(2 - W)} \tag{11}$$

*2.2.8.1.2. Methodology proposed by Snyder (1992)*

*2.2.8.1.3. Methodology proposed by Bernardo et al. (1996)*

*2.2.8.1.4. Methodology proposed byAllen et al. (1998)*

**2.3. Evaluation of methods**

based on the equations 17, 18, 19 and 20:

*D*

<sup>2</sup> *Kt* =+ - + 0,482 0,024ln ( ) 0,000376 0,0045 *F U RU* (14)

<sup>2</sup> *Kt* =- + + - 0,108 0,0286 0,0422ln ( ) 1434ln ( ) 0,000631 ln ( ) ln ( ) *U F RU* é ù ë û *F RU* (16)

Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the…

Where U2 is the wind speed at 2 m height in km/day, RU is the average relative humidity (%), and F is the boundary of the green crop area, considered in this study equal to 15 m.

To evaluate the performance of the methods we proceeded to linear regression analysis, considering the linear model y = bx (regression through the origin), in which the independ‐ ent variable was the Penman-Monteith (EToPM), and the dependent variable, the other meth‐ ods. Was also used the Index of agreement of Willmott (D) (Willmott, 1981), the mean absolute error (MAE), the maximum error (EMAX) and the efficiency of the method (EF),

( ) <sup>1</sup>

å

*n i*


*n i*

2

(| | ( |)

*Pi O Oi O*


( )*in*

2 2 2

()( ) ( )

*O O* -+ - <sup>=</sup> å å

Where: O = estimated values by EToPM, Pi = estimated by other methods; *O*¯= mean value EToPM.

*O O O Pi EF*

*Pi Oi*

2

<sup>å</sup> (17)

<sup>1</sup> ( ) *<sup>n</sup> MAE Oi Pi <sup>i</sup> <sup>n</sup>* = - <sup>å</sup> (18)

*<sup>n</sup> EMAX MAX Oi Pi* = - (19)

å (20)

*Kt* = 0,69 (15)

2

http://dx.doi.org/10.5772/52278

267

Where:

ETo - Evapotranspiration from the wet surface (mm/day) during the sunshine period;

G - heat flux in the soil (MJ/m2 /day) during the diurnal period;

Rn - diurnal net radiation at a vegetated surface (MJ/m2 /day), and

W - tangent of water the vapor saturation pressure curve at the point of diurnal daily mean airtemperature (Tair).

#### *2.2.8. Class A Pan Method (TCA)*

The ETo is estimated by the Class "A" Pan by using the following equation:

$$
\dot{E} \, E \, \text{To} \, ^{\text{TCA}} = E V. \, \text{Kt} \tag{12}
$$

Where: Ev - Evaporation of Class A Pan, in mm dia-1 and Kt, the Pan coefficient (dimension‐ less).

#### *2.2.8.1. Methods to estimate the Pan coefficient – Kt*

To estimate the Pan coefficient - Kt method used in the Class "A" Pan were evaluated four methodologies are described below:

*2.2.8.1.1. Methodology proposed by Cuenca (1989)*

$$\begin{aligned} \text{Kt} &= 0, 475-2, 4.10^{-4} \,\text{U}\_2 + 5, 16.10^{-3} \,\text{H} + 1, 8.10^{-3} \,\text{.}\,\text{F}-1, 6.10^{-5} \,\text{.}\,\text{R}\boldsymbol{\Omega}^2 \\ &- 1, 01.10^{-6} \,\text{.}\,\text{F}^2 - 8, 0.10^{-9} \,\text{R}\boldsymbol{\Omega}^2 \,\text{.}\,\text{U}\_2 - 1, 0.10^{-8} \,\text{.}\,\text{R}\boldsymbol{\Omega}^2 \,\text{.}\,\text{F} \end{aligned} \tag{13}$$

*2.2.8.1.2. Methodology proposed by Snyder (1992)*

ues of evapotranspiration rates thatare more representative of the water vapor transfer proc‐ ess to the atmosphere for a givenagricultural ecosystem. In addition, the classical expression of the Bowen ratio (b) was modifiedherein by considering the sensible heat flux (H) emer‐ gent from the evaporative surface inconjunction with the air turbulent flux, which trans‐ ports also latent heat flux (LE). Such procedureresults in a similarity between the aerodynamic resistances of sensible heat and latent heat fluxes soas to allow for a considera‐

ETo estimated by the SPM proposed by Villa Nova et al. (2006) was obtained from equation

( ) 0,408 (2 ) *Rn G ETo*

/day) during the diurnal period;

W - tangent of water the vapor saturation pressure curve at the point of diurnal daily mean

Where: Ev - Evaporation of Class A Pan, in mm dia-1 and Kt, the Pan coefficient (dimension‐

To estimate the Pan coefficient - Kt method used in the Class "A" Pan were evaluated four

4 3 3 52



ETo - Evapotranspiration from the wet surface (mm/day) during the sunshine period;

The ETo is estimated by the Class "A" Pan by using the following equation:

*W*


/day), and

. *TCA ETo EV Kt* = (12)

ble simplification without impairing the estimates.

Rn - diurnal net radiation at a vegetated surface (MJ/m2

*2.2.8.1. Methods to estimate the Pan coefficient – Kt*

*2.2.8.1.1. Methodology proposed by Cuenca (1989)*

2

1,01.10 . 8,0.10 . 1,0.10 . .


62 9 2 8 2 2

0,475 2,4.10 5,16.10 . 1,8.10 . 1,6.10 .

*Kt U H F RU F RU U RU F*

methodologies are described below:

11:

Where:

less).

G - heat flux in the soil (MJ/m2

*2.2.8. Class A Pan Method (TCA)*

airtemperature (Tair).

266 Evapotranspiration - An Overview

$$\text{Kt} = 0,482 + 0,024\ln\left(F\right) - 0,000376\,\text{L}\_2 + 0,0045\,\text{R}\,\text{L}\,\text{H}\tag{14}$$

*2.2.8.1.3. Methodology proposed by Bernardo et al. (1996)*

$$Kt = 0, \Theta \Theta \tag{15}$$

*2.2.8.1.4. Methodology proposed byAllen et al. (1998)*

$$Kt = 0,108 - 0,0286\,\mathrm{L}\_2 + 0,0422\,\mathrm{ln}\,(F) + 1434\,\mathrm{ln}\,(RLI) - 0,000631 \Big[\ln\left(F\right)\Big]^2 \ln\left(RLI\right) \tag{16}$$

Where U2 is the wind speed at 2 m height in km/day, RU is the average relative humidity (%), and F is the boundary of the green crop area, considered in this study equal to 15 m.

#### **2.3. Evaluation of methods**

To evaluate the performance of the methods we proceeded to linear regression analysis, considering the linear model y = bx (regression through the origin), in which the independ‐ ent variable was the Penman-Monteith (EToPM), and the dependent variable, the other meth‐ ods. Was also used the Index of agreement of Willmott (D) (Willmott, 1981), the mean absolute error (MAE), the maximum error (EMAX) and the efficiency of the method (EF), based on the equations 17, 18, 19 and 20:

$$D = 1 - \frac{\sum\_{i}^{n} (Pi - O\bar{\imath})^2}{\sum\_{i}^{n} (\lfloorPi\bar{\imath} - \overline{O}\rfloor + \{O\bar{\imath} - \overline{O}\})^2} \tag{17}$$

$$MAE = \frac{1}{n} \sum\_{i} \text{\textquotedblleft} (\text{Oi} - \text{Pi}) \tag{18}$$

$$EXAX = MAX(\left|\text{Ci} - \text{Pi}\right|)\_{in}^{n} \tag{19}$$

$$EF = \frac{\sum (O - \overline{O})^2 + \sum (O - Pi)^2}{\sum (O - \overline{O})^2} \tag{20}$$

Where: O = estimated values by EToPM, Pi = estimated by other methods; *O*¯= mean value EToPM.

### **3. Results and discussion**

### **3.1. Comparison of Penman-Monteith with other methods**

Table 1 shows the monthly averages of air temperature, the relative humidity, wind speed and solar radiation for the ten years of data analyzed.

mum error (EMAX) and the slope (b) comparing the parameterized Penman-Monteith meth‐ od (FAO PM) with other methodologies and Figure 2, the graphs of correlation in respect to

Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the…

MAE (mm d-1)

1 H-S 0.84 0.95 0.46 0.83 2.18 1.02

5 H-S 0.91 0.97 0.29 0.90 1.42 1.02

10 H-S 0.93 0.80 0.24 0.93 1.24 1.02

1 RS-FAO 0.92 0.98 0.38 0.89 1.56 0.94

5 RS-FAO 0.95 0.99 0.26 0.93 1.06 0.95

10 RS-FAO 0.96 0.99 0.22 0.95 0.90 0.96

1 MAK 0.93 0.89 0.82 0.60 2.37 1.23

5 MAK 0.96 0.87 0.82 0.51 1.81 1.23

10 MAK 0.97 0.87 0.82 0.48 1.59 1.24

1 J-H 0.92 0.89 1.00 0.34 2.80 0.80

5 J-H 0.94 0.88 0.95 0.23 2.39 0.81

10 J-H 0.95 0.87 0.95 0.19 2.28 0.81

1 LIN 0.54 0,78 0,84 0,51 3,08 0.95

5 LIN 0.64 0,83 0,68 0,60 2,05 0.94

10 LIN 0.67 0,85 0,63 0,62 1,79 0.94

1 MSP 0.89 0.93 0.66 0.72 2.45 1.16

5 MSP 0.91 0.93 0.66 0.68 1.85 1.16

10 MSP 0.92 0.93 0.66 0.67 1.45 1.16

**Table 2.** Analysis of statistical methods for estimating evapotranspiration for averaging periods of 1, 5 and 10 days.

EF (mm d-1)

EMAX (mm d-1)

http://dx.doi.org/10.5772/52278

**b**

269

**Methods R2 D**

the line 1:1.

Periods (days)


**Table 1.** Average monthly values of air temperature (Tar), relative humidity (RU), wind speed at 2m (U2) and solar radiation (Rs) for 1996 to 2006 period.

These meteorological variables are required as input data to the standard method and esti‐ mation of other variables, as well as entries for the other methods tested. Evapotranspiration is a complex phenomenon and non-linear, because it is dependent on the interaction be‐ tween various climatological elements (Kumar et al, 2002).

Table 2 shows the parameters for statistical analysis: correlation coefficient (r2 ), index of agreement of Wilmott (D), mean absolute error (MAE), efficiency of the method (EF), maxi‐


**3. Results and discussion**

268 Evapotranspiration - An Overview

**Months**

radiation (Rs) for 1996 to 2006 period.

tween various climatological elements (Kumar et al, 2002).

**3.1. Comparison of Penman-Monteith with other methods**

Tair (ºC)

and solar radiation for the ten years of data analyzed.

Table 1 shows the monthly averages of air temperature, the relative humidity, wind speed

RU (%)

January 26.47 74.35 2.36 305

February 26.54 73.55 2.12 296

March 25.69 75.75 1.73 247

April 24.41 76.70 1.54 207

May 21.85 75.16 1.50 176

June 20.98 77.41 1.51 159

July 20.28 76.35 1.68 160

August 21.60 75.90 2.24 194

September 22.16 75.80 2.43 209

October 23.07 75.90 2.31 227

November 24,29 76,19 2,34 251

December 25,79 75,99 2,21 281

**Table 1.** Average monthly values of air temperature (Tar), relative humidity (RU), wind speed at 2m (U2) and solar

Table 2 shows the parameters for statistical analysis: correlation coefficient (r2

These meteorological variables are required as input data to the standard method and esti‐ mation of other variables, as well as entries for the other methods tested. Evapotranspiration is a complex phenomenon and non-linear, because it is dependent on the interaction be‐

agreement of Wilmott (D), mean absolute error (MAE), efficiency of the method (EF), maxi‐

U2 (m s-1)

Rs (W m-2)

), index of


**Table 2.** Analysis of statistical methods for estimating evapotranspiration for averaging periods of 1, 5 and 10 days.

all methods. This finding agrees with Mendonça (2001, 2003) justified by smoothing the averages of the sampled values. Another observation concerning the increment of the re‐ maining days is that on the Hargreaves-Samani, Solar Radiation-FAO and Linacre, the mean absolute error (MAE) suffered a decrement. For the method of Hargreaves-Samani, this range was 0.46 mm d-1 (for the period of 1 day) going to 0.24 mm dia-1 (for 10 days). For the FAO-24 solar radiation method, the variation was of 0.38 mm d-1 (within 1 day) to 0.22 mm

Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the…

Makkink method and Simplified Penman method showed no variation in the mean absolute error, keeping them constant in d-1 0.82 mm and 0.66 mm d-1 for all periods, respectively. Since the Jensen-Haise method presented the MAE of 1.00, 0.96 and 0.95 mm d-1, respective‐

Analyzing the slopes of the methods evaluated was observed that Makkink and Simplified Penman Method showed values above 1 for all periods, with the group of methods overesti‐ mated ETo-PM. These results agree with those observed by Mendonça (2001; 2003) and Fer‐

In the group of methods that are underestimated ETo FAO-24 Radiation, Jensen-Haise and Linacre. Observing Table 2, can be seen that the maximum error (EMAX) obtained similar behavior to EMA, decreasing as you increase the periods analyzed. The greater EMAX ob‐ served for a period of 1 day was the method of Linacre, equal 3.08 mm d-1. Also for this method was the largest decrease in EMAX, when will the period 1 to10 days, with 1.79 mm

As for efficiency, it is clear that the methods of Hargreaves-Samaniand FAO-24 Radiation remained throughout the period evaluated with EF greater than 0.82. These methods also showed the best adjustment of the index of agreement ofWilmontt, and FAO-24 Radiation

The Simplified Penman method received a satisfactory performance for the estimation of

compared EToPM, a situation similar to that found by Villa Nova et al. (2006). The rate of

The Simplified Penman and Makkink methods decreased efficiency over the period ana‐ lyzed. EF were their best for the period of 1 day (0.72 to 0.60 mm d-1, respectively) was lower for 10 days (0.66 and 0.47 mm d-1, respectively.) as for the concordance index Wil‐ montt(D), Makkink values decreased from 0.89 (for the 1 day period) going to 0.86 for the period of 10 days. Simplified Penman method showed D constant for periods of 1, 5 and 10 days (0.93) Linacre was efficient and index D increased with the increase of the peri‐ ods analyzed, as can be seen in table 1. Jensen-Haise showed EF decreasing with the in‐ crease of the evaluation period, with the worst rates of EF methods (ranging from 0.34 for 1 day, to 0.17 in 10 days). The index D remained above 0.86, D being its highest rate for

agreement Wilmontt observed for this method was greater than 0.90 (D = 0.93).

of 0.89, showing a small dispersion

http://dx.doi.org/10.5772/52278

271

d-1 at 10 days. To Linacre method, the same variation was from 0.84 to 0.63 mm d-1.

ly, for periods of 1, 5 and 10 days.

d-1 for this period.

the period of 1 day (0.89).

nandes (2006), assessments in the same area of study.

coming to D index of 0.99, for periods of 5 and 10 days.

ETo in the study region, for the daily period, with r2

**Figure 2.** Graphs of correction in respect to the line 1:1.

Observing the values in Table 2 and Figure 2, it appears that all methods were evaluated value of the correction coefficient (r2 ) larger than 0.80, with the exception of the method of Linacre, where r2 values to the two periods varied from 0.54 (for 1 day) to 0.67 (for 10 days). This adjustment increased r2 , a measure that increased the periods studied was common to all methods. This finding agrees with Mendonça (2001, 2003) justified by smoothing the averages of the sampled values. Another observation concerning the increment of the re‐ maining days is that on the Hargreaves-Samani, Solar Radiation-FAO and Linacre, the mean absolute error (MAE) suffered a decrement. For the method of Hargreaves-Samani, this range was 0.46 mm d-1 (for the period of 1 day) going to 0.24 mm dia-1 (for 10 days). For the FAO-24 solar radiation method, the variation was of 0.38 mm d-1 (within 1 day) to 0.22 mm d-1 at 10 days. To Linacre method, the same variation was from 0.84 to 0.63 mm d-1.

Makkink method and Simplified Penman method showed no variation in the mean absolute error, keeping them constant in d-1 0.82 mm and 0.66 mm d-1 for all periods, respectively. Since the Jensen-Haise method presented the MAE of 1.00, 0.96 and 0.95 mm d-1, respective‐ ly, for periods of 1, 5 and 10 days.

Analyzing the slopes of the methods evaluated was observed that Makkink and Simplified Penman Method showed values above 1 for all periods, with the group of methods overesti‐ mated ETo-PM. These results agree with those observed by Mendonça (2001; 2003) and Fer‐ nandes (2006), assessments in the same area of study.

In the group of methods that are underestimated ETo FAO-24 Radiation, Jensen-Haise and Linacre. Observing Table 2, can be seen that the maximum error (EMAX) obtained similar behavior to EMA, decreasing as you increase the periods analyzed. The greater EMAX ob‐ served for a period of 1 day was the method of Linacre, equal 3.08 mm d-1. Also for this method was the largest decrease in EMAX, when will the period 1 to10 days, with 1.79 mm d-1 for this period.

As for efficiency, it is clear that the methods of Hargreaves-Samaniand FAO-24 Radiation remained throughout the period evaluated with EF greater than 0.82. These methods also showed the best adjustment of the index of agreement ofWilmontt, and FAO-24 Radiation coming to D index of 0.99, for periods of 5 and 10 days.

The Simplified Penman method received a satisfactory performance for the estimation of ETo in the study region, for the daily period, with r2 of 0.89, showing a small dispersion compared EToPM, a situation similar to that found by Villa Nova et al. (2006). The rate of agreement Wilmontt observed for this method was greater than 0.90 (D = 0.93).

The Simplified Penman and Makkink methods decreased efficiency over the period ana‐ lyzed. EF were their best for the period of 1 day (0.72 to 0.60 mm d-1, respectively) was lower for 10 days (0.66 and 0.47 mm d-1, respectively.) as for the concordance index Wil‐ montt(D), Makkink values decreased from 0.89 (for the 1 day period) going to 0.86 for the period of 10 days. Simplified Penman method showed D constant for periods of 1, 5 and 10 days (0.93) Linacre was efficient and index D increased with the increase of the peri‐ ods analyzed, as can be seen in table 1. Jensen-Haise showed EF decreasing with the in‐ crease of the evaluation period, with the worst rates of EF methods (ranging from 0.34 for 1 day, to 0.17 in 10 days). The index D remained above 0.86, D being its highest rate for the period of 1 day (0.89).

**Figure 2.** Graphs of correction in respect to the line 1:1.

value of the correction coefficient (r2

This adjustment increased r2

270 Evapotranspiration - An Overview

Observing the values in Table 2 and Figure 2, it appears that all methods were evaluated

Linacre, where r2 values to the two periods varied from 0.54 (for 1 day) to 0.67 (for 10 days).

) larger than 0.80, with the exception of the method of

, a measure that increased the periods studied was common to

### **3.2. Comparison of methods for estimating the Kt**

Table 3 shows the results of statistical analysis of different methodologies for determining the coefficient of the Pan (Kt) used in the Class "A" Pan method and Figure 3, the graphs of correlation in respect to the line 1:1


**Table 3.** Analysis of statistical methods of different methodologies for determining the coefficient of the Pan (Kt) for estimating evapotranspiration for averaging periods of 1, 5 and 10 days.

**Figure 3.** Graphs of correlation in respect to the line 1:1.

as does the method of Snyder (b = 0.89).

Cuenca, 0.90 mm d-1.

It was also found that all methods showed an increase in the value of efficiency (EF) as it increased the period and those proposed by Allen, Snyder and Cuenca, overestimated ETo-PM at all times. The methodology presented Allen, from 5 days a slope (b) constant at 0.95,

Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the…

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273

The mean absolute error (MAE) of all methods decreased as the periods analyzed increased, and the method of Cuenca presented the lowest MAE (0.22 mm d-1) for the period of 10 days. Methodologies for determining the assessed value of Kt, the worst results were ob‐ tained by the method of Snyder, the value of its efficiency (EF) 0.63, 0.74 and 0.75, respec‐ tively stop for a period of about 1, 5 and 10 days, while other methods reached levels higher than EF 0.90. This same method was maximum error (EMAX) decrease as you increased the periods analyzed, however, persisted for 10 days at 1.62 mm d-1, while for the same period the methodology proposed by Allen reached 1.17 mm. d-1, Bernardo et al., 1.07 mm d-1 and

Looking at Table 3 and Figure 3 can see an increase in the coefficient of correlation (r2 ) as it increases the evaluation period and all the methods used to determine the coefficient of the Pan (Kt) present good adjustment r2 , were above 0.80 in all periods. These results agree with those found by Conceição (2002; 2005) who compared the monthly ETo estimated by the Class "A" Pan with the Penman-Monteith-FAO and Mendonça et al. (2006) who compared the daily ETo estimated.

It is observed that the best method for determining Kt on a daily, and subsequent conver‐ sion of EV with ETO was proposed by Cuenca with EF = 0.81, followed by Bernardo, EF = 0.79. However, for the same period of 1 day, the index of agreement of Wilmontt of the two methods presented the same amount (D = 0.95).

Reference Evapotranspiration (ETo) in North Fluminense, Rio de Janeiro, Brazil: A Review of Methodologies of the… http://dx.doi.org/10.5772/52278 273

**Figure 3.** Graphs of correlation in respect to the line 1:1.

**3.2. Comparison of methods for estimating the Kt**

(TCA) **r2 <sup>D</sup>**

estimating evapotranspiration for averaging periods of 1, 5 and 10 days.

Pan (Kt) present good adjustment r2

methods presented the same amount (D = 0.95).

the daily ETo estimated.

correlation in respect to the line 1:1

Methods

Periods (days)

272 Evapotranspiration - An Overview

Table 3 shows the results of statistical analysis of different methodologies for determining the coefficient of the Pan (Kt) used in the Class "A" Pan method and Figure 3, the graphs of

> MAE (mm d-1)

1 Allen 0.81 0.95 0.53 0.77 2.14 0.94

5 Allen 0.95 0.98 0.31 0.90 1.36 0.95

10 Allen 0.95 0.98 0.27 0.92 1.17 0.95

1 Bernardo 0.80 0.95 0.53 0.79 1.78 1.03

5 Bernardo 0.92 0.97 0.33 0.89 1.31 1.05

10 Bernardo 0.94 0.98 0.30 0.91 1.07 1.05

1 Cuenca 0.81 0.95 0.50 0.81 1.83 0.97

5 Cuenca 0.91 0.98 0.26 0.93 1.08 0.98

10 Cuenca 0.95 0.99 0.22 0.95 0.90 0.99

1 Synder 0.81 0,92 0,69 0,63 2,68 0.88

5 Synder 0.93 0,94 0,53 0,74 1,78 0.89

10 Synder 0.95 0,95 0,51 0,75 1,62 0.89

**Table 3.** Analysis of statistical methods of different methodologies for determining the coefficient of the Pan (Kt) for

increases the evaluation period and all the methods used to determine the coefficient of the

those found by Conceição (2002; 2005) who compared the monthly ETo estimated by the Class "A" Pan with the Penman-Monteith-FAO and Mendonça et al. (2006) who compared

It is observed that the best method for determining Kt on a daily, and subsequent conver‐ sion of EV with ETO was proposed by Cuenca with EF = 0.81, followed by Bernardo, EF = 0.79. However, for the same period of 1 day, the index of agreement of Wilmontt of the two

Looking at Table 3 and Figure 3 can see an increase in the coefficient of correlation (r2

EF (mm d-1)

, were above 0.80 in all periods. These results agree with

EMAX (mm d-1)

**b**

) as it

It was also found that all methods showed an increase in the value of efficiency (EF) as it increased the period and those proposed by Allen, Snyder and Cuenca, overestimated ETo-PM at all times. The methodology presented Allen, from 5 days a slope (b) constant at 0.95, as does the method of Snyder (b = 0.89).

The mean absolute error (MAE) of all methods decreased as the periods analyzed increased, and the method of Cuenca presented the lowest MAE (0.22 mm d-1) for the period of 10 days. Methodologies for determining the assessed value of Kt, the worst results were ob‐ tained by the method of Snyder, the value of its efficiency (EF) 0.63, 0.74 and 0.75, respec‐ tively stop for a period of about 1, 5 and 10 days, while other methods reached levels higher than EF 0.90. This same method was maximum error (EMAX) decrease as you increased the periods analyzed, however, persisted for 10 days at 1.62 mm d-1, while for the same period the methodology proposed by Allen reached 1.17 mm. d-1, Bernardo et al., 1.07 mm d-1 and Cuenca, 0.90 mm d-1.

### **4. Conclusions**

Based on the results obtained in this work can be concluded that all indirect methods as‐ sessed showed improvements in their statistical indices as they increased the periods of analysis. It can be concluded that the methods of Makkink, Jansen-Haise, Linacre and Class "A" Pan using the methodology proposed by Snyder for obtaining Kt did not achieve satis‐ factory levels and should not be adopted for the estimation of reference evapotranspiration (ETo) in the study area. Otherwise, the methods of Hargreaves-Samani, FAO-24Solar Radia‐ tion, Simplified Penman Method and Class "A" Pan using the methodology proposed by Cuenca for obtaining Kt presented the best adjustment for the evaluation period and can be used satisfactorily for the estimation of ETo in the North Fluminense, Rio de Janeiro, Brazil.

[4] Conceição, M. A. F. Reference Evapotranspiration Based on Class A Pan Evapora‐

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### **Acknowledgements**

The authors are grateful for the National Counsel for Scientific and Technological Develop‐ ment – CNPq; the Coordenação de Aperfeiçoamento de Pessoal de Nível superior – CAPES and the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro – FAPERJ, for the financial support and logistics that made these studies possible.

### **Author details**

José Carlos Mendonça\* , Barbara dos Santos Esteves and Elias Fernandes de Sousa

\*Address all correspondence to: mendonca@uenf.br; barbbarase@gmail.com; efs@uenf.br

Laboratory of Agricultural Engineering (LEAG / UENF), Rio de Janeiro, Brazil

### **References**


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**4. Conclusions**

274 Evapotranspiration - An Overview

**Acknowledgements**

**Author details**

**References**

José Carlos Mendonça\*

Paper 56, 300p. 1998.

Based on the results obtained in this work can be concluded that all indirect methods as‐ sessed showed improvements in their statistical indices as they increased the periods of analysis. It can be concluded that the methods of Makkink, Jansen-Haise, Linacre and Class "A" Pan using the methodology proposed by Snyder for obtaining Kt did not achieve satis‐ factory levels and should not be adopted for the estimation of reference evapotranspiration (ETo) in the study area. Otherwise, the methods of Hargreaves-Samani, FAO-24Solar Radia‐ tion, Simplified Penman Method and Class "A" Pan using the methodology proposed by Cuenca for obtaining Kt presented the best adjustment for the evaluation period and can be used satisfactorily for the estimation of ETo in the North Fluminense, Rio de Janeiro, Brazil.

The authors are grateful for the National Counsel for Scientific and Technological Develop‐ ment – CNPq; the Coordenação de Aperfeiçoamento de Pessoal de Nível superior – CAPES and the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro –

\*Address all correspondence to: mendonca@uenf.br; barbbarase@gmail.com; efs@uenf.br

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[3] Burman, R. D.; Nixon, P. R.; Wright, J. L.; Pruitt, W. O. Chapter 6, Water require‐ ments. In: Design and operation of farm irrigation systems. ASCE Monography, No

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, Barbara dos Santos Esteves and Elias Fernandes de Sousa

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## *Edited by Stavros G. Alexandris and Ruzica Stricevic*

Evapotranspiration - An Overview contains recent advances in the physics of evaporation and transpiration from a typical experimental site to large scale areas. It incorporates many years of authors experience with the latest research on the methods and the models used worldwide, engaging advanced technology and modern instrumentation. he reader benefits from the in-depth analysis and the diverse sites and settings, where the models, applications and methods are tested. Weather conditions, soil moisture, geology, climatic systems are examined for their role and influence on the theoretical and actual water demand by the atmosphere in the earth's ecosystem. his book not only provides students and scientists with the information to improve the procedures for estimating evapotranspiration, but will also help them to manage and evaluate the observed data.

Photo by jessicahyde / iStock

Evapotranspiration - An Overview

Evapotranspiration

An Overview

*Edited by Stavros G. Alexandris*