# Seasonal and Diurnal Variations in the Priestley–Taylor Coefficient for a Large Ephemeral Lake

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{−2}during both periods, and the root mean square errors were much smaller than the average evaporation measurements at daily scale. U-shaped diurnal patterns of α were found during both periods, due partly to the negative correlation between α and the available energy (A). Compared to the vapor pressure deficit (VPD), wind speed (u) exerts a larger contribution to these variations. In addition, u is positively correlated with α during both periods, however, VPD was positively and negatively correlated with α during the high-water and low-water periods, respectively. Subdaily α exhibited contrasting clusters in the (u, VPD) plane under the same available energy ranges. Our study highlights the seasonal and diurnal course of α and suggests the careful use of PTE at subdaily scales.

## 1. Introduction

^{2}) across the globe [10], 10 of which are located in China. Poyang Lake is the largest freshwater lake (3680 km

^{2}) in China. The surrounding area of Poyang Lake serves as an important food production base for approximately 10 million people [11]. However, due to hydrological droughts, Poyang Lake’s surface area has decreased in the past three decades [12], which may have great negative impacts on the regional economy and natural ecosystem.

_{n}) during the wetland-covered period, but is out of phase with R

_{n}during the water-covered period in Poyang Lake, indicating that diurnal α may experience substantial variations during the water-covered period. As reported in previous studies [23,24], α can be larger than 2 and smaller than 0.5. In addition, the driving forces of ET differ under water-covered and wetland-covered conditions across different temporal scales [28]. In this paper, we study the seasonal and diurnal variations in α and explore their controlling factors in Poyang Lake. Although many studies have discussed the variations in α over water bodies or wetlands, few studies have compared the α variations between water bodies and wetlands. The substantial changes in the water level in Poyang Lake (~8–20 m) provide natural experimentation settings for studying the variations in α and their controlling factors under changing surface conditions. Whether the same value of α is feasible for both water bodies and wetlands and whether the same factors control the variations in α are the main topics of this paper.

## 2. Background and General Definitions

_{eq}) under such saturated conditions. E

_{eq}can be theoretically determined as the available energy flux (A) times Δ/(Δ+γ) because the Bowen ratio (B = H/LE) equals γ/Δ in this case, where Δ is the slope of the saturated vapor pressure to the air temperature and γ is the psychrometric constant. Δ and γ are the functions of air temperature and air pressure, respectively. The actual evaporation from wide water surfaces and wetlands is estimated using the concept of equilibrium evaporation and the coefficient α to account for the effect of the drying power of the air on evaporation (Equation (1)). Because A equals R

_{n}− G, α is, therefore, written as Equation (2), where EF is the evaporative fraction (EF = LE/(H + LE)). EF is assumed to be insensitive to wind speed in equilibrium conditions due to the similarity of evaporation and heat conduction [29,30]. The surface heat flux (G) is the heat flux that is conducted from the surface into the water (or from water body to the surface). Due to the high heat capacity of the water body [5,6], the G of lake systems usually takes up a large proportion of the surface energy balance [31,32,33].

_{a}), which is estimated by the product of the vapor pressure deficit and a function of wind speed. γ/(Δ+γ) represents the fraction of the drying power that transfers into latent heat flux. When the vapor pressure deficit tends to be zero, Equation (3) tends to be E

_{eq}.

_{a}if the available energy flux remains constant. Similarly, α decreases with an increase of the available energy flux if the other factors remain constant.

## 3. Data and Processing

#### 3.1. Site Description

^{2}in summer to less than 1000 km

^{2}in winter [35,36]. The major river routes are covered by water throughout the year, whereas most of the lake basin is only covered by water during the high-water period. The lake periodically reveals its bottom surfaces (i.e., mudflat, grassland, etc.), during the low-water period. The measuring system in this study was set in a periodically inundated zone of Poyang Lake, which changes from a water surface to a wetland periodically within a year.

_{0},y

_{0}). A footprint analysis using the Kljun model [39,40] reveals that the major source area (85%) was within 1~2 km of the wind direction under unstable conditions. Compared to unstable conditions, the extent of the 85% source area was larger under stable conditions. However, the major source area was still within 6 km in most cases except when the surface layer was extremely stable (Z

_{m}/L

_{0}> 1, Z

_{m}is the measuring height and L

_{0}is the Monin–Obukhov length). Data were discarded when Z

_{m}/L

_{0}> 1. Due to the relatively small area of the island (less than 1 km

^{2}), the flux contribution from Sheshan Island can be ignored because it is usually small, less than 5% from the major northwest winds (Figure 2B). The water coverage fractions within the EC footprints were generally larger than 90% and smaller than 20% during the high-water and low-water periods, respectively [27]. The data used in this paper are deposited in a public domain repository (https://figshare.com/articles/data_water-12-00849/11968551).

#### 3.2. Data Processing

_{2}/H

_{2}O analyzer and a 3-D Sonic Anemometer (EC150, Campbell Scientific Inc., Logan, UT, USA). The eddy covariance technique and subsequent corrections were then used to estimate the 30 min scale H and LE using the high-frequency measurements of departures from the mean values. H and LE were calculated using the following equations (Equation (4) and Equation (5)):

^{−3}), c

_{p}is the specific heat of dry air (J·g

^{−1}·K

^{−1}), and λ is the latent heat of vaporization (J·g

^{−1}), which is dependent on the air temperature. w′, T′, and q′ are the deviations from the time-averaged vertical wind velocity (m·s

^{−1}), air temperature (K), and water vapor density (g·m

^{−3}), respectively. In addition, the meteorological forcings were measured at a 30 min scale. The surface radiation components, including the downward/upward short-wave and long-wave radiations, were measured by the pyrgeometers/pyranometers (CNR4, Kipp & Zonen B.V., Delft, The Netherlands). The air temperature and relative humidity were measured by an HMP155A (Vaisala, Helsinki, Finland).

_{1}, x

_{2}, …, x

_{i}, …, x

_{n}) from the model at each step based on the statistical significance of the term in the regression. P

_{coeff}is the p-value of the estimated coefficient of a candidate term x

_{i}. A potential predicted term is accepted in the final regression model (status set as ′′In′′) if P

_{coeff}and P

_{F}are smaller than the threshold of 0.05. The stepwise analysis was conducted using MATLAB 2015b.

## 4. Results and Discussion

#### 4.1. Environmental Conditions and Energy Fluxes

_{s}↓, R

_{l}↓, A, T

_{a}, VPD, and u were 282.1 W·m

^{−2}, 420.5 W·m

^{−2}, 111.3 W·m

^{−2}, 297.0 K, 6.1 hPa, and 4.6 m/s, respectively, in the high-water period, which were larger than those in the low-water period (i.e., 235.4 W·m

^{−2}, 351.2 W·m

^{−2}, 73.7 W·m

^{−2}, 285.7 K, 3.7 hPa, and 3.8 m/s, respectively). Unimodal seasonal patterns (Figure 3) were observed for the available energy and most of the meteorological variables (i.e., R

_{s}↓, R

_{l}↓, T

_{a}, and VPD). Although the wind speed was also larger for the high-water period than for the low-water period (4.6 m/s vs. 3.8 m/s), compared to T

_{a}, the wind speed exhibited a reduced trend and larger variations throughout the year.

_{s}↓, R

_{l}↓, and T

_{a}). LE peaked in the summer (376.1 W·m

^{−2}), and the minimum value (−26.9 W·m

^{−2}) occurred in the winter. Compared to LE, H displayed an opposite trend with a smaller mean (11.3 W·m

^{−2}) in the high-water period than that in the low-water period (16.9 W·m

^{−2}), although the available energy was larger when the water level was higher (92.2 W·m

^{−2}vs. 62.7 W·m

^{−2}on average) (Table 1). One reason for the smaller H in the summer is that a larger portion of the available energy was consumed by LE (EF

_{mean}= 0.86, EF = LE/(H + LE)) in the high-water period than that (EF

_{mean}= 0.71) in the low-water period.

#### 4.2. Seasonal and Diurnal Variations in α

#### 4.3. The Controlling Factors of Parameter α

^{−2}during the high-water period (e.g., Figure 9E).

## 5. Discussion

#### 5.1. Contributions of Local Advection and Energy Control to the α Variations

_{a}if the available energy remains constant under water-surface conditions. We estimated the contributions of VPD and u to the α variations by multiplying the standard deviations in VPD and u with their respective coefficients of VPD and u from Table 3. The results are shown in Table 4. Compared to wind speed, VPD exerted much smaller effects on α during the high-water period (i.e., 0.06 vs. 0.11 at a daily scale) (Table 4). This result may be because evaporation from the lake exerted feedbacks on the ambient air humidity. Therefore, a low VPD (small atmospheric demand) does not necessarily indicate that the evaporation is small. Instead, a small VPD may be the result of a large latent heat flux from the lake.

_{a}if the air temperature and available energy remain constant. As Granger and Gray [42] noted, VPD reflects the moisture conditions of an unsaturated surface to some extent (i.e., a higher VPD indicates a drier surface). Therefore, this complementary effect may be responsible for the negative correlation between α and VPD during the low-water period.

^{−2}, respectively). The corresponding α at those timings was 1.32, 1.09, and 1.07, respectively. In the morning, u was relatively large and VPD was relatively small; thus, the point at 8:00 is located below the y = ax + b line. Further, u decreases and VPD increases with time (Figure 8). Therefore, points at 11:00 and 11:30 are located above the y = ax + b line, and α remained relatively low (1.09 and 1.07) at noon. In summary, because u decreases and VPD increases with time during the day (Figure 8), the points in Figure 9 and Figure 10 tend to rotate in a counterclockwise direction in the u–VPD plane. Because wind speed makes the most (positive) contribution to diurnal α variations (Table 4), clusters of subdaily α in different (u, VPD) regions were found.

#### 5.2. Use of the PT Equation in Changing Surface Conditions

^{−2}, indicating that the PT equation is feasible in estimating the overall latent heat flux of Poyang Lake at an annual scale. In addition, the root mean square error (RMSE) of the LE predictions at a daily scale was much smaller than the mean measurements in LE, indicating that the PT equation (with α as 1.26) is capable of modeling seasonal ET variations. Worth noting, the RMSE of the LE predictions at a 30 min scale was still less than 50% of the mean ET measurements during the water-covered period. Considerations of the diurnal courses of α and the impacts of wind speed are needed to better model LE at a 30 min scale, especially during the wetland-covered period.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The extent of Poyang Lake and the measuring site in Sheshan Island. The middle panel shows the Landsat 8 images (composites using bands 5, 4, and 3 of the Operational Land Imager, which emphasize the distribution of the water body and vegetation) acquired on 24 August (high-water) and 13 February (low-water). The lower panel shows pictures of the measuring site during the high-water and low-water periods.

**Figure 2.**Footprint analysis for the eddy covariance measurement. (

**A**) Cumulative footprint from the wind direction; (

**B**) distribution of the wind direction; (

**C**) source area under stable conditions, where the median values of wind speed were used in the calculation; (

**D**) the source area under unstable conditions, where the median values of wind speed were used in the calculation.

**Figure 3.**A–E are seasonal variations in meteorological variables, including the incoming shortwave and longwave radiation (

**A**), the available energy (

**B**), air temperature (

**C**), VPD (

**D**), and wind speed (

**E**). Water level variations at Xingzi station are shown in (

**F)**, where black and red lines represent the daily values in 2015 and the averaged daily values during the period of 1950–2015, respectively.

**Figure 4.**Seasonal variations in H, LE, and EF in 2015. The outliers of EF when H + LE was close to 0 are not shown in the figure.

**Figure 5.**Diurnal variations in H and LE in 2015. (

**A**) and (

**C**) indicate the high-water period, and (

**B**) and (

**D**) indicate the low-water period. The length of the bar in each subfigure represents the value of the standard deviation of the energy fluxes.

**Figure 7.**Diurnal variations in α during the high-water (

**A**) and low-water (

**B**) periods in 2015. The length of the bar in each subfigure represents the value of the standard deviation of the variable.

**Figure 8.**Diurnal variations in A, VPD, and u during the high-water (

**A**,

**C**,

**E**) and low-water (

**B**,

**D**,

**F**) periods in 2015. The length of the bar in each subfigure represents the value of the standard deviation of the variable.

**Figure 9.**Distributions of 30 min scale α with respect to VPD and wind speed under a range of available energy conditions during high-water period.

**Figure 10.**Distributions of 30 min scale α with respect to VPD and wind speed under a range of available energy conditions during the low-water period.

Variables | The Entire Period | High-Water Period | Low-Water Period | ||||||
---|---|---|---|---|---|---|---|---|---|

Min | Max | Mean | Min | Max | Mean | Min | Max | Mean | |

H (W·m^{−2}) | −17.5 | 96.8 | 16.3 | −13.8 | 96.8 | 11.3 | −17.5 | 75.4 | 16.9 |

LE (W·m^{−2}) | −26.9 | 376.1 | 68.9 | −12.6 | 376.1 | 80.9 | −26.9 | 351.1 | 45.8 |

EF (-) | −3.78 | 2.13 | 0.81 | −1.07 | 1.73 | 0.86 | −3.78 | 2.13 | 0.71 |

Time scales | The Entire Period | High-Water Period | Low-Water Period | ||||||
---|---|---|---|---|---|---|---|---|---|

Min | Max | Mean | Min | Max | Mean | Min | Max | Mean | |

Daily | 0.22 | 2.29 | 1.27 | 0.69 | 2.29 | 1.25 | 0.22 | 2.26 | 1.29 |

Subdaily | 0.01 | 2.12 | 1.29 | 0.16 | 2.11 | 1.27 | 0.01 | 2.12 | 1.30 |

**Table 3.**Stepwise regression analysis for α during both the high-water and low-water periods at daily and subdaily scales. RMSE represents the root mean squared error of the prediction from the regression equation. r represents the correlation coefficient between the predictions and “ground-truth” α.

Timescales | Variables | Statistics for Coefficients | Statistics for the Regression Equation | |||
---|---|---|---|---|---|---|

Daily | High-water | Coefficients | Status | P_{coeff} | RMSE | r |

A | −0.0016 | In | <0.001 | 0.146 | 0.66 | |

VPD | 0.0148 | In | 0.001 | |||

u | 0.0465 | In | <0.001 | |||

Constant | 1.102 | |||||

Low-water | Coefficients | Status | P_{coeff} | RMSE | R^{2} | |

A | −9.503 × 10^{−4} | Out | 0.106 | 0.256 | 0.58 | |

VPD | −0.0340 | In | <0.001 | |||

u | 0.084 | In | <0.001 | |||

Constant | 1.096 | |||||

30 min | High-water | Coefficients | Status | P_{coeff} | RMSE | R^{2} |

A | −8.730 × 10^{−4} | In | <0.001 | 0.214 | 0.46 | |

VPD | 0.0098 | In | <0.001 | |||

u | 0.0317 | In | <0.001 | |||

Constant | 1.168 | |||||

Low-water | Coefficients | Status | P_{coeff} | RMSE | R^{2} | |

A | −0.0015 | In | <0.001 | 0.329 | 0.47 | |

VPD | −0.0065 | In | 0.02 | |||

u | 0.0573 | In | <0.001 | |||

Constant | 1.197 |

Variables | Daily | 30 min | ||
---|---|---|---|---|

High-Water | Low-Water | High-Water | Low-Water | |

VPD | 0.06 | −0.08 | 0.05 | −0.02 |

u | 0.11 | 0.16 | 0.08 | 0.13 |

A | −0.12 | 0 | −0.09 | −0.12 |

Time Scales | High-Water | Low-Water | ||||
---|---|---|---|---|---|---|

RMSE (W·m^{−2}) | Bias (W·m^{−2}) | Mean (W·m^{−2}) | RMSE (W·m^{−2}) | Bias (W·m^{−2}) | Mean (W·m^{−2}) | |

Daily | 11.2 | 3.4 | 105.9 | 19.1 | 1.5 | 70.4 |

30 min | 23.3 | 4.1 | 105.9 | 28.4 | 4.2 | 70.4 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gan, G.; Liu, Y.; Pan, X.; Zhao, X.; Li, M.; Wang, S.
Seasonal and Diurnal Variations in the Priestley–Taylor Coefficient for a Large Ephemeral Lake. *Water* **2020**, *12*, 849.
https://doi.org/10.3390/w12030849

**AMA Style**

Gan G, Liu Y, Pan X, Zhao X, Li M, Wang S.
Seasonal and Diurnal Variations in the Priestley–Taylor Coefficient for a Large Ephemeral Lake. *Water*. 2020; 12(3):849.
https://doi.org/10.3390/w12030849

**Chicago/Turabian Style**

Gan, Guojing, Yuanbo Liu, Xin Pan, Xiaosong Zhao, Mei Li, and Shigang Wang.
2020. "Seasonal and Diurnal Variations in the Priestley–Taylor Coefficient for a Large Ephemeral Lake" *Water* 12, no. 3: 849.
https://doi.org/10.3390/w12030849