# Evaluation of Potential Evapotranspiration Based on CMADS Reanalysis Dataset over China

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data and Study Area

_{max}), daily minimum temperature (T

_{min}), relative humidity (RH), solar radiation (Rs), and wind speed at 10m height (u

_{10}) to estimate PET using PM. PET values derived from the CMADS datasets (PET_cma) were compared with PET_obs values and differences are referred to as under or overestimation (PET_cma < PET_obs or PET_cma > PET_obs).

#### 2.2. Penman–Monteith Equation for Potential Evapotranspiration

^{−1}and albedo of 0.23 [50]. The daily potential evapotranspiration (PET, mm/day) estimated by the Penman–Monteith equation (PM) is:

_{n}is the net radiation at the crop surface (MJ m

^{−2}day

^{−1}); G is the soil heat flux density (MJ m

^{−2}day

^{−1}), which is assumed to be zero as the magnitude of G, in this case, is relatively small; T

_{mean}is the mean daily air temperature (°C); u

_{2}is the wind speed at 2 m height (m s

^{−1}); e

_{s}is the saturation vapor pressure (kPa); e

_{a}is the actual vapor pressure (kPa); e

_{s}− e

_{a}is the vapor pressure deficit (kPa); Δ is the slope of the relationship between saturation vapor pressure and mean daily air temperature (kPa °C

^{−1}); γ is the psychrometric constant which depends on the altitude of each location (kPa °C

^{−1}).

_{s}is the mean of the saturation vapor pressure at T

_{max}and T

_{min}; e

_{a}was calculated by multiplying the average values of the saturation vapor pressure at T

_{max}and T

_{min}by the mean daily relative humidity. The FAO recommendation is to calculate the actual vapor pressure by taking the average the product of vapor pressure at the higher temperature and daily low humidity and the product of vapor pressure at the lower temperature and the daily high humidity. However, only the mean relative humidity is available from the CMADS datasets, and in the case of missing maximum and minimum relative humidity, Equation (4) was used.

_{max}and T

_{min}are daily maximum and minimum temperatures; e

_{(Tmax)}and e

_{(Tmin)}are the saturation vapor pressures at daily minimum temperature and daily maximum temperature; and T is the temperature. Using Equation (2), the saturation vapor pressure at the daily maximum and minimum air temperatures can be calculated by:

_{n}is the net radiation which is expressed as the difference between the incoming net shortwave radiation (R

_{ns}) and the outgoing net long wave radiation (R

_{nt}):

_{ns}is computed by:

_{s}is the solar radiation which is either computed the from the daily solar duration (n), using the Ångström–Prescott radiation equation (see Equation (9)) for the weather station data or is obtained directly from CMADS.

_{a}is the extraterrestrial radiation which is calculated from the solar constant, the solar declination, and the time of the year as suggested by the FAO (the recommended values a

_{s}= 0.25 and b

_{s}= 0.5 are used in this study); n is the actual solar duration; N is the maximum possible solar duration which is related to the latitude and can be computed using the sunset hour angle in radians; and $\frac{n}{N}$ is the relative solar duration. The outgoing net long wave radiation (R

_{nt}) is derived by the Stefan–Boltzmann law.

#### 2.3. Evaluation Method

^{2}), the normalized root mean square error (NRMSE), and the skill score (S

_{score}). PB is a basic measure used to assess average annual PET and seasonal patterns of PET which provide an overview of the performance of the two models. For a more comprehensive analysis, R

^{2}, NRMSE, and S

_{score}are used to analyze the performance of daily, monthly, and annual PET_cma.

_{i}are PET_cma and the O

_{i}are PET_obs.

^{2}shows how well PET_cma approximates the real data points (PET_obs). It indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Ordinary least squares regression is used to fit the line to the data. The ideal fitted line is found when R

^{2}is very close to 1. Linear regression is suitable for a long time series. We have data for nine years, so R

^{2}is appropriate to use for daily and monthly PET_cma. R

^{2}is given by:

_{score}indicates the common area of the probability distribution function (PDF) of PET_cma and PET_obs. It is the cumulative minimum value of the two distributions at each binned value. The equation is:

_{M}and Z

_{O}are the frequency values in a given bin from PET_cma and PET_obs.

_{max}, T

_{min}, R

_{h}, R

_{s}, and u

_{10}. The control is PET_obs, which used all the input parameters with data from the weather stations. For comparison, we singly examine each input parameter as an independent variable using CMADS data, covering the same area and time period, for the variable instead of the weather station data while keeping the observed weather station data for all other input parameters.

## 3. Results

#### 3.1. Spatial and Seasonal Patterns of Average Annual PET

#### 3.2. Evaluation of the Performance with Multiple Indicators

^{2}, and S

_{score}are used to identify the variation in PET estimates with daily and monthly time scales. R

^{2}and S

_{score}can be used to indicate differences at an annual scale, but the CMADS datasets cover only nine years, which is not long enough for adequate linear regression. Thus, annual behavior is only measured by NRMSE as reference. The three measures are used for all the stations. Figure 6 shows the cumulative distribution functions (CDF) of the measures for different time scales. The CDF for NMRSE shows that the estimate given by PET_cma is best at an annual time scale. It decreases as the time scale gets finer, but the difference is not very large. Almost 100% of the stations are <0.4 for every time scale. Up to 80% stations are <0.18, <0.23, and <0.27 for annual, monthly, and daily time scales, respectively. The R

^{2}values also show similar results for monthly and daily time scales with the monthly CDF better than the daily CDF. For 99% of the stations, monthly and daily R

^{2}values are >0.90 and >0.80. S

_{score}shows that the difference between monthly and daily time scales is very small, but it has a broader range than the other two measures. The monthly and daily S

_{score}values for most stations (99%) are >0.70 and >0.75, respectively.

#### 3.3. Effect of Different Variables on the Bias in Estimation of the PET

_{max}, T

_{min}, and R

_{h}were the independent variables. This indicates that errors in T

_{max}, T

_{min}, and R

_{h}from the CMADS data contributed little to the bias in PET_cma. Figure 7 shows that wind speed and solar radiation contribute to the error in PET_cma in different ways. When wind speed is the independent variable, PET is underestimated, and percentage bias is in the range −15% to −5%. Most underestimated values are found in eastern China. For solar radiation, R

_{s}, PET is mainly overestimated with percentage bias in the range 5% to 30% over most of the area. In central and western China the overestimation is greater, with percentage bias predominantly in the range 15% to 30%.

_{s}was the independent variable. When elevation increased, the lower boundary of percentage bias also increased. When elevation was >2000 m, the percentage bias of PET is >10%. Larger percentage bias, >20%, is found mainly for stations with PET_obs in the range 750–1250 mm. Windspeed, which causes underestimation of PET, and solar radiation, which causes overestimation of PET, offset each other, reducing the overestimation of PET_cma.

## 4. Discussion

## 5. Conclusions

^{2}, and S

_{score}consistently show that the annual PET_cma values are better than those at shorter time scales when compared with PET_obs.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Mean seasonal potential evapotranspiration estimated from weather station data (PET_obs, (

**a**)), CMADS datasets (PET_cma, (

**b**)) with their histograms (

**c**).

**Figure 4.**Spatial distribution of percentage bias, indicating the accuracy of average annual PET_cma values (

**a**), and frequency distribution of percentage bias (

**b**).

**Figure 5.**Spatial distribution of percentage bias showing the accuracy of mean seasonal potential evapotranspiration (PET) estimated using CMADS datasets, PET_cma (

**a**) and the frequency distribution of percentage bias (

**b**).

**Figure 6.**Cumulative distribution functions of the statistical measures NRMSE (

**a**), R

^{2}(

**b**), and S

_{score}(

**c**) indicating the accuracy of monthly and daily PET_cma estimates compared to PET_obs.

**Figure 7.**Spatial distribution of percentage bias showing the effects of maximum temperature (

**a**), minimum temperature (

**b**), wind speed (

**c**), solar radiation (

**d**), and relative humidity (

**e**) on the bias of PET_cma.

**Figure 8.**Relationship between elevation, PET_obs, and errors indicated by percentage bias for wind speed (

**a**) and solar radiation (

**b**).

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**MDPI and ACS Style**

Tian, Y.; Zhang, K.; Xu, Y.-P.; Gao, X.; Wang, J.
Evaluation of Potential Evapotranspiration Based on CMADS Reanalysis Dataset over China. *Water* **2018**, *10*, 1126.
https://doi.org/10.3390/w10091126

**AMA Style**

Tian Y, Zhang K, Xu Y-P, Gao X, Wang J.
Evaluation of Potential Evapotranspiration Based on CMADS Reanalysis Dataset over China. *Water*. 2018; 10(9):1126.
https://doi.org/10.3390/w10091126

**Chicago/Turabian Style**

Tian, Ye, Kejun Zhang, Yue-Ping Xu, Xichao Gao, and Jie Wang.
2018. "Evaluation of Potential Evapotranspiration Based on CMADS Reanalysis Dataset over China" *Water* 10, no. 9: 1126.
https://doi.org/10.3390/w10091126