# Parameterization of Evapotranspiration Estimation for Two Typical East Asian Crops

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{A}), the water vapor pressure deficit (VPD), and air temperature (T), can be measured or derived from routine weather observation, while the aerodynamic resistance (r

_{a}) can be estimated from the vegetation height and the wind velocity with its measurement height [5]. However, the determination of the surface resistance r

_{s}is one of the major difficulties in the application of the PM model [3,6].

_{s}can be estimated as a quotient of mean stomatal resistance and active leaf area index [5]. However, this approach (abbreviated as the PM-FAO approach) does not take into account the dependence of r

_{s}on meteorological variables [7]. Therefore, Katerji and Perrier [8] proposed a simple linear model (abbreviated as the PM-KP approach in this study), accounting for the influence of meteorological variables and aerodynamic resistance on r

_{s}. Compared with other methods, the PM-KP approach has the advantage of its simplicity (e.g., the calibration requires no more data than routine weather observation and eddy-covariance measurement) and its good performance across a variety of croplands. Moreover, the PM-KP approach takes r

_{a}into account as an influencing factor on r

_{s}, assuming that r

_{s}is a combination of the resistance of all leaves, the resistance of the soil surface, and the resistance between these surfaces and the “big leaf” where r

_{a}plays a role. However, some studies noted that the PM-KP model performs well for well-watered crops and for short periods of time within which the surface vegetation and weather do not change much [9], while other studies reported that the PM-KP approach has also been adapted to soil water stress conditions and to surfaces that are fully and partially covered by crops [7]. Most studies on the PM-KP approach in the literature (e.g., [10,11,12,13]) have mainly been focused on well-watered crop surfaces in Mediterranean regions because of the scarce water resources and over irrigation in agriculture managements in these regions [14].

## 2. Methods

#### 2.1. Research Sites and Field Campaigns

_{g}), and net radiation (R

_{n}), were measured by Automatic Weather Stations (WS-GP1, Delta-T Devices Ltd., Cambridge, UK) and a net radiometer (NR-LITE, Campbell Scientific Inc., Logan, UT, USA). Leaf area index (LAI) was biweekly measured by a destructive sampling method using a leaf area meter (LI-3000A, LI-COR Inc., Lincoln, NE, USA). The canopy height of crops was biweekly determined as the mean of the heights of five plants randomly sampled out of the largest canopy heights covering 10% of the area [20].

_{H}) and latent heat (Q

_{E}) between the surface and the atmosphere were determined by eddy-covariance (EC) technique. EC measurement was equipped with an ultrasonic anemometer (USA-1, METEK GmbH, Elmshorn, Germany) and a fast-response open-path infrared analyzer (LI-7500, LI-COR Inc., Lincoln, NE, USA), both working at a sampling frequency of 20 Hz at 2.5-m height above ground level in the potato field and 2.8-m height above the flooded water level in the rice field. The EC software package TK3 [21] post-processed the high-frequency raw data according to all international agreed procedures [22]. Half-hourly aggregated sensible and latent heat fluxes with quality flags [23] were available as results. Data-quality selection criteria were applied in this study in order to examine time series of fluxes and generate a high-quality database [24]. The internal boundary layer estimation and footprint analysis were performed so as to compute the contribution from the target surface [25,26]. In the rice field, the fetch ranged from 37 m (northwest) to 60 m (northeast), generating the internal boundary layer height ranging from 3.0 m to 3.9 m and 68% to 82% of the flux contributed by the rice field. In the potato field, the fetch ranged from 18 m (northwest) to 102 m (east), generating the internal boundary layer height ranging from 2.1 m to 5.0 m and 51% to 99% of the flux contributed by the potato field. Turbulent flux data were then marked as irrelevant records when flux contribution from the target land-use type was less than 70% and the aerodynamic measurement height was higher than the internal boundary layer. Finally, the 30-min dataset, excluding low quality data, irrelevant records, and outliers by a multiple-step filter [24], was used as the high-quality database for subsequent parameterization. For further information about the field campaign, please refer to [27,28].

^{−1}or mm day

^{−1}), Q

_{E}(W m

^{−2}) can be converted into the amount of liquid evaporated into vapor if simply divided by the latent heat of vaporization. Thus, both ET and Q

_{E}are unambiguously used in this study.

#### 2.2. Correction for Energy Balance Closure

_{G}is the ground heat flux, estimated as 14% and 50% of R

_{n}for daytime and nighttime, respectively, [29] in this study, and ΔQ is the stored heat in the canopy, which is usually small and assumed to be negligible [30]. The imbalance in Equation (1), often found when Q

_{H}and Q

_{E}are obtained from the measurement by the EC technique [31,32,33], can be significantly compensated with the contribution from secondary circulations which can hardly be measured by the EC system [31,34]. This study followed the energy balance closure (EBC) correction suggested by Charuchittipan et al. [34]:

_{p}is the specific heat of air, λ is the heat of evaporation for water, and superscripts indicate the measurement or correction methods. Bo

^{EBC-HB}is the corrected Bowen ratio, which should be either calculated iteratively until it converges [34] or calculated by solving Equation (2), which results in the analytic solution:

_{2}is positive) is partitioned into Q

_{H}when Bo > 0.07, because buoyancy mainly transports Q

_{H}rather than Q

_{E}near the surface.

#### 2.3. Penman-Monteith Equation

_{s}is the saturated vapor pressure; s

_{c}is the slope of the saturation vapor-pressure curve; e

_{a}is the partial vapor pressure of the air; ρ is the air density; and γ is the psychometric constant.

_{E}by Equation (4) requires the parameterization of r

_{a}and r

_{s}. The estimation of r

_{a}can be performed as [5].

_{om}is the roughness height for momentum, approximated as 0.123h; z

_{oh}is the roughness height for water vapor, approximated as 0.1z

_{om}.

_{s}can be estimated by a LAI-dependent approach [5]:

_{si}is the stomatal resistance of a single well-illuminated leaf, and LAI

_{active}is the LAI of the active sunlit leaves, which is generally the upper part of the canopy and can be estimated as LAI

_{active}= 0.5 LAI. Although r

_{si}was suggested to be 70 to 80 s m

^{−1}for estimation of hourly or shorter-time-based Q

_{E}for agricultural crops [4], this study evaluated site-specific values of r

_{si}and used the PM-FAO approach as reference.

_{s}can be parameterized by the establishment of a linear relationship between r

_{s}/r

_{a}and r*/r

_{a}:

_{s}is determined experimentally from the half-hourly observations by inverting the PM equation:

#### 2.4. Sensitivity Test

_{E}resulting from the relative change in the i-th variable V

_{i}. A positive/negative S

_{i}indicates that Q

_{E}increases/decreases with the increase of V

_{i}. A larger absolute value of S

_{i}indicates stronger influence of V

_{i}on Q

_{E}.

_{A}, VPD, r

_{s}, and r

_{a}can be calculated as:

_{i}and P

_{i}indicate the i-th observation and prediction, respectively, and the overbar indicates the mean. The optimal parameters for the best model performance could then be determined with the highest value of NSeff.

_{ip}) is the sum of the i-th original value (X

_{io}), a constant systematic bias (E

_{s}), and a random error with zero-mean and normally distribution (E

_{r}):

_{r}) and the unbiased relative standard error (SEE

_{r}), respectively:

_{error}and ET

_{original}are half-hourly ET for the perturbed and original dataset, respectively; overbar means the mean of the entire observation period; and n is the number of observations.

## 3. Results

#### 3.1. Meteorological Conditions and Vegetation Development

^{2}m

^{−2}per day in late July, and the canopy height increased from 0.3 m to 0.8 m in the rice field. From the beginning of the mid-season period in August, the rice grains emerged, the green leaves decreased, and the canopy height was consistently around 0.9 m until harvest. The potato started a rapid growth in June, when LAI increased from 0.5 m

^{2}m

^{−2}to 4 m

^{2}m

^{−2}and the canopy height from 0.15 m to 0.6 m within just one month. The maximum increasing rate of LAI was 0.21 m

^{2}m

^{−2}per day in the development stage of potato. In the subsequent mid- and late-seasons, new potato tubers grew and green leaves declined until all green leaves disappeared with a canopy height of 0.1 m at the end of the growing season.

#### 3.2. Sensitivity Coefficients

_{A}, VPD, r

_{a}, and r

_{s}on simulated ET by the PM model were calculated on a half-hourly base. Then the data in the daytime through the growing season were taken into account to derive the mean values for diurnal and seasonal patterns (Figure 2).

_{QA}and S

_{VPD}were positive. The available energy uniformly played a primary role in the variation of ET simulation. It determined 50% to 80% of the ET variation throughout most of the day. As the sum of S

_{QA}and S

_{VPD}is unity, these two coefficients showed opposite diurnal patterns. S

_{VPD}ranged between 20% and 40% in most hours, and had values even larger than S

_{QA}in the early morning and later afternoon. S

_{r}

_{a}was almost constantly small, with a range between −17% and 3%, most of which were negative. S

_{r}

_{s}was constantly negative, ranging between −48% and −14% with the highest absolute values in the early morning and late afternoon. The increase of Q

_{A}, VPD, and the decrease of r

_{s}resulted in the increase of ET, while r

_{a}had a minor influence on ET. The seasonal patterns of the sensitivity coefficients showed generally consistent results with the diurnal mean. Furthermore, the sensitivity coefficients showed insignificant seasonal variation, probably because the permanent standing water in the rice field acted as a major source of ET.

_{VPD}had a range between 15% and 78%, with the maximum occurring in the late afternoon. S

_{r}

_{a}was positive in most hours of the day, with relatively large values around 20% in the morning, and decreased to around zero in the afternoon. S

_{r}

_{s}was constantly negative and determined 32% to 68% of ET variation. Differently from the rice field, the sensitivity coefficients for the potato field showed significant seasonal variations. The monthly mean of S

_{VPD}in July was 41%, which was larger than those in June (32%) and August (30%). However, S

_{r}

_{s}showed the opposite trend, with the minimum monthly mean of 33% in July, smaller than those in June (46%) and August (42%). S

_{r}

_{a}had small negative values, with absolute mean value of 8% in July, and positive values with mean values of 14% in June and 11% in August. As the surface vegetation changed greatly in the potato field and there was large seasonal variation in precipitation (Figure 1), the seasonal variation in the sensitivity coefficients could possibly result from the dependence of ET on the surface vegetation and water stress.

_{s}, besides Q

_{A}and VPD, played a very important role in ET estimation by the PM model. It had even more influence on ET than VPD for the potato field. As Q

_{A}and VPD can be accurately obtained from the field observation with modern devices, the estimation of r

_{s}is a key step for the PM model.

#### 3.3. PM-KP Calibration Coefficients

_{s}/r

_{a}and r*/r

_{a}(Equation (7)) for each site. As it was demonstrated that 20 values of hourly data were sufficient for a reliable calibration in the literature [7,43], this study randomly sampled 40 half-hourly records out of the daytime high quality data (in total, 594 records from the potato site and 361 from the rice site) for calibration. Such calibration procedure was repeated for 1000 runs so as to yield the statistical distributions of a and b, which are shown in Figure 3.

_{r}per systematic error ratio) as to b (~3.0% BIAS

_{r}per systematic error ratio) for the rice site, and slightly more sensitive to b (~7.6% BIAS

_{r}per systematic error ratio) than to a (~5.4% BIAS

_{r}per error ratio) for the potato site. The PM-KP model was nearly twice as sensitive to systematic errors in a and b for the potato field as for the rice field. Random errors (Figure 4B,D) showed less effect to the PM-KP model performance in comparison with systematic errors. Only ~1.9% SEE

_{r}per random error ratio in both a and b was found for the rice field, and 3.4% and 4.0% SEE

_{r}per random error ratio in a and b, respectively, for the potato field.

#### 3.4. Optimization of PM-FAO Approach

_{si}from 0 to 320 s m

^{−1}[44] for both sites (Figure 5). The model efficiency coefficient was obviously changed with the varied value of r

_{si}. For the potato site, the model efficiency coefficient showed a peak value of NSeff = 0.81 at r

_{si}= 117 s m

^{−1}(Figure 5 solid line). Either an increase or decrease of r

_{si}resulted in a sharp decrease in NSeff = 0.6 at r

_{si}= 320 s m

^{−1}or NSeff < 0 at r

_{si}< 20 s m

^{−1}. When using the literature values of r

_{si}between 70 and 80 s m

^{−1}[4], NSeff ranged from 0.72 to 0.77, therefore r

_{si}= 117 s m

^{−1}was used as an optimal estimation for the potato site in this study. If compared with using r

_{si}= 75 s m

^{−1}(the medium of the literature values [4]) which resulted in NSeff = 0.75 and regression slope (Q

_{E}

^{PM-FAO}against Q

_{E}

^{EBC-HB}) of 1.06 (n = 1061), the model performance was slightly improved by using r

_{si}= 117 s m

^{−1}, with a smaller regression slope of 0.94. The decline of the slope was due to the larger value of r

_{si}, resulting in an increase of the denominator of the PM function and consequently the decrease of the simulated Q

_{E}.

_{si}of 38 s m

^{−1}with NSeff = 0.91 (Figure 5 dotted line) and regression slope (Q

_{E}

^{PM-FAO}against Q

_{E}

^{EBC-HB}) of 0.96 (n = 847). This optimal value of r

_{si}was much smaller than the typical range of r

_{si}in the literature (e.g., [4]) and resulted in better model performance than using the medium of literature value of r

_{si}= 75 s m

^{−1}which resulted in NSeff = 0.80 and regression slope of 0.80. The values of the slope lower than unity indicated that the PM-FAO approach had a tendency to underestimate Q

_{E}for the rice field in this study, especially in the case of large values of Q

_{E}.

_{si}were used to estimate ET as a comparison so as to evaluate the performance of PM-KP approach in the subsequent sections.

#### 3.5. Performance of PM-KP Approach

^{−1}for u, ±5% for RH, ±0.25 m

^{2}m

^{−2}for LAI, ±0.05 m for h, and ±5 days for day of the year (DOY). An individual NSeff within each interval window was obtained from the Q

_{E}

^{PM-KP}, Q

_{E}

^{PM-FAO}, and Q

_{E}

^{EBC-HB}values which fell in the given interval window. For instance, NSeff at T = 10 °C displayed in Figure 6 was calculated from those Q

_{E}

^{PM-FAO}and Q

_{E}

^{EBC-HB}values when T ranged between 7.5 and 12.5 °C.

^{−1}. In contrast, the performances of both models showed greater variation with humidity. The model efficiency was very low when the air was dry. Good performances of both models were achieved at high relative humidity (RH > 50%), well developed vegetation (LAI > 1.5 m

^{2}m

^{−2}), and tall plant height (h > 0.3 m), with NSeff > 0.8. Actually, these humid conditions coincided with fully developed vegetation from mid-June to July (DOY 170 to 210), resulting in good performance of the models for the potato field in the summer monsoon. The performance of the PM-KP approach for poorly developed vegetation surface (LAI < 1.5 m

^{2}m

^{−2}) and short plant (h < 0.3 m) in August (DOY > 210) was better than that of the PM-FAO approach.

^{2}m

^{−2}, h > 0.6 m). This was because low temperature was only observed in the early morning at the early growing stage of rice, which coincided with the occurrence of poorly developed vegetation, and small Q

_{E}. Windy conditions with u > 1.5 m s

^{−1}resulted in a better simulation of the PM-KP model than the PM-FAO model, because Q

_{E}is expected to be enhanced under windy conditions on sunny days in summer, but this effect is insufficiently represented by the PM-FAO approach with the dependence of r

_{s}only on LAI [45]. The open standing water, as an evident source of evaporation in the rice field, is apparently unrelated to stomata.

## 4. Discussion

_{s}when LAI was very small, whereas the flooded rice field for small LAI was almost an open water surface and the actual r

_{s}was close to zero, thus r

_{s}was much overestimated by the PM-FAO approach. The PM-KP approach had the advantage because it was consistent with the fact that Q

_{E}is dominantly controlled by the meteorological factors rather than LAI in well-irrigated crops [45]. It was reported that the calibration of the FAO-KP approach is species-specific [48] and the coefficient a and b need calibration for (1) well-watered crops in the development growth stage; (2) well-watered crops in the senescence stage; and (3) water-stressed crops during the development stage [8,14,43]. On one hand, our study on the distribution of a and b and the error analysis agrees well with these situations. On the other hand, a and b are not sensitive to the variety of the vegetation development in the rice field, and can be considered to be constant for the entire growing season of rice.

_{s}decreases linearly with log(VPD) for plant species and stomatal sensitivity is proportional to the magnitude of 1/r

_{s}at low VPD (≤10 hPa) [49], which was later demonstrated to be consistent with the linear model presented by [50]. High temperature as well as high VPD in the afternoon in dry pre-monsoon season leads to a high evapotranspiration rate and then to a stomatal closure for potato plants in the research region [28]. This regulation could result in a deviation of r

_{s}from the estimation by Equations (6) and (7), and consequently the poor efficiency of both the PM-KP approach and the PM-FAO approach in the case of the dry air. In the future, the Asian summer monsoon is predicted to be extended and rainfall to be increased in the research region [51]. Therefore, it could be expected that the rain-fed croplands like potato fields would be better watered, and the VPD influence on stomatal closure would be weakened, and the PM-KP could perform better for this region.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Meteorological conditions and vegetation development at the research sites, including daily mean air temperature (T, solid line in

**A**), daily mean relative humidity (RH, dashed line in

**A**), daily sum precipitation (P, solid line in

**B**), daily mean solar radiation (R

_{g}, dashed line in

**B**), and leaf area index (LAI, dashed line representing potato and solid line representing rice in

**C**with standard deviations as error bars), and plant height (dashed line representing potato and solid line representing rice in

**D**).

**Figure 2.**Diurnal (

**A**,

**B**) and seasonal (

**C**,

**D**) patterns of Penman-Monteith model sensitivity coefficients for available energy (closed circle), vapor pressure deficit (VPD, open circle), aerodynamic resistance (cross), and stomatal resistance (closed square) in the rice field (

**A**,

**C**) and in the potato field (

**B**,

**D**).

**Figure 3.**Statistical distribution of the regression coefficients

**a**and

**b**of the Penman-Monteith-Katerji-Perrier (PM-KP) approach for the potato site (

**upper**) and the rice site (

**lower**).

**Figure 4.**Sensitivity of PM-KP modelled evapotranspiration to systematic errors (

**A**,

**C**) and random errors (

**B**,

**D**) in PM-KP coefficients a (solid line with closed circle) and b (dotted line with open circle) for the potato site (

**A**,

**B**) and the rice site (

**C**,

**D**).

**Figure 5.**Nash-Sutcliffe model efficiency coefficient (NSeff) of PM-FAO (Penman-Monteith-Food and Agriculture Organization) modelled Q

_{E}to modifications in r

_{si}for the potato field (solid line) and rice field (dotted line).

**Figure 6.**Nash-Sutcliffe model efficiency coefficient (NSeff) of simulated evapotranspiration by PM-FAO approach (solid line with closed circle) and PM-KP approach (dash line with open circle) against air temperature (T), wind speed (u), relative humidity (RH), leaf area index (LAI), plant height (h), and day of the year (DOY), for the potato field.

**Figure 7.**Nash-Sutcliffe model efficiency coefficient (NSeff) of simulated evapotranspiration by the PM-FAO approach (solid line with closed circle) and the PM-KP approach (dash line with open circle) against air temperature (T), wind speed (u), relative humidity (RH), leaf area index (LAI), plant height (h), and day of the year (DOY), for the rice field.

Species | LAI (m^{2} m^{−2}) | Crop Height (m) | a | b | References |
---|---|---|---|---|---|

Alfalfa | NA | NA | 0.31 | 0.25 | [8] |

Clementine | 2.1–2.6 | 4.08 ± 0.23 | 0.23 | 0.0042 | [10] |

Grain sorghum | NA | NA | 0.56 ± 0.12 | 0.6 ± 0.7 | [46] |

Grass | 2–2.5 | 0.1 | 0.16 ± 0.02 | 0 ± 0.02 | [43,46] |

Lettuce | NA | 0.15–0.20 | 0.73 | −0.58 | [9,14] |

Oats | NA | NA | 0.88 | 3.39 | [47] |

Soybean | 2–4 | 0.8 | 0.95 | 1.55 | [43] |

Sunflower | NA | NA | 0.45 ± 0.06 | 0.2 ± 0.35 | [46] |

Sweet sorghum | 3–6.4 | 2 | 0.84 | 1.00 | [7,43] |

Tomato | 0.5–3.8 | 0.7 | 0.54 ± 0.1 | 2.4 ± 1.2 | [7] |

Vineyard | 2–2.8 | 2.2 | 0.91 | 0.45 | [43] |

Wheat | 2.5–3.1 | 1 | 0.96 | 4.24 | [47] |

Rice | 0–5.8 | 0.3–0.9 | 0.52 ± 0.08 | −0.06 ± 0.14 | this study |

Potato | 0–4 | 0–0.6 | 0.63 ± 0.21 | 1.47 ± 0.42 | this study |

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**MDPI and ACS Style**

Zhao, P.; Lüers, J.
Parameterization of Evapotranspiration Estimation for Two Typical East Asian Crops. *Atmosphere* **2017**, *8*, 111.
https://doi.org/10.3390/atmos8060111

**AMA Style**

Zhao P, Lüers J.
Parameterization of Evapotranspiration Estimation for Two Typical East Asian Crops. *Atmosphere*. 2017; 8(6):111.
https://doi.org/10.3390/atmos8060111

**Chicago/Turabian Style**

Zhao, Peng, and Johannes Lüers.
2017. "Parameterization of Evapotranspiration Estimation for Two Typical East Asian Crops" *Atmosphere* 8, no. 6: 111.
https://doi.org/10.3390/atmos8060111