Prediction of Biome-Specific Potential Evapotranspiration in Mongolia under a Scarcity of Weather Data

Abstract

We propose practical guidelines to predict biome-specific potential evapotranspiration (ET_p) from the knowledge of grass-reference evapotranspiration (ET₀) and a crop coefficient (K_c) in Mongolia. A paucity of land-based weather data hampers use of the Penman–Monteith equation (FAO-56 PM) based on the Food and Agriculture Organization (FAO) guidelines to predict daily ET₀. We found that the application of the Hargreaves equation provides ET₀ estimates very similar to those from the FAO-56 PM approach. The K_c value is tabulated only for crops in the FAO-56 guidelines but is unavailable for steppe grasslands. Therefore, we proposed a new crop coefficient, K_{c adj} defined by (a) net solar radiation in the Gobi Desert (K_{c adjD}) or (b) leaf area index in the steppe region (K_{c adjS}) in Mongolia. The mean annual ET_p obtained using our approach was compared to that obtained by FAO-56 guidelines for forages (not steppe) based on tabulated K_c values in 41 locations in Mongolia. We found the differences are acceptable (RMSE of 0.40 mm d⁻¹) in northern Mongolia under high vegetation cover but rather high (RMSE of 1.69 and 2.65 mm d⁻¹) in central and southern Mongolia. The FAO aridity index (AI) is empirically related to the ET_p/ET₀ ratio. Approximately 80% and 54% reduction of ET₀ was reported in the Gobi Desert and in the steppe locations, respectively. Our proposed K_{c adj} can be further improved by considering local weather data and plant phenological characteristics.

1. Introduction

Groundwater represents a vital water resource for ecosystems within an arid continental climate. Management of this resource relies on the knowledge of groundwater recharge (GR). However, in vast territories such as Mongolia, direct measurements of GR are unrealistic because they involve excessive costs from time-consuming and labor-intensive efforts. The use of hydrological models for simulating the water balance (and GR) within the groundwater–soil–plant–atmosphere continuum represents a valid alternative to direct measurements if the soil hydraulic properties and vegetation characteristics are properly assessed and initial and boundary conditions are well-known [1]. The main advantage of modeling is that the user needs only crop-specific potential evapotranspiration (ET_p) and precipitation (P) for obtaining simulations of GR. Precipitation measurements are commonly available and reasonably accurate. In contrast, obtaining a reliable prediction of ET_p represents a challenge in countries with limited availability of land-based, full suite weather data. This ET_p may be estimated by multiplying a grass-reference crop evapotranspiration (ET₀) by a time-variant crop coefficient, K_c [2]. The reference grass is defined as a hypothetical crop with a height of 0.12 m, a surface resistance of 70 s m⁻¹, and an albedo of 0.23 in a well-watered field [2]. Subsequently, ET_p is partitioned into potential evaporation (E_p) and potential transpiration (T_p) depending on the knowledge of leaf area index (LAI) or vegetation cover fraction.

The concept of potential evapotranspiration is broadly used in hydrology and supported by established methods and software packages that account for non “well-watered” soil moisture conditions (e.g., HYDRUS [3] and MODFLOW [4]). The E_p and P represent the system-dependent boundary conditions of the hydrologic model over the soil profile, while T_p refers to potential root water uptake. Therefore, a reliable prediction of ET_p is fundamental in numerical models for obtaining the GR and actual evapotranspiration (ET_a) that represents a reduction of ET_p induced by water stress.

The available models to estimate ET₀ can be classified as: (i) full physically based models describing mass and energy conservation principles; (ii) semi-physically based models that deal with either mass or energy conservation; and (iii) black-box models based on empirical relationships and machine learning algorithms [5,6,7]. The Penman–Monteith equation, based on the Food and Agriculture Organization (FAO) guidelines (FAO-56 PM), is internationally recognized as the standard approach for computing ET₀ [2,8]. This equation is considered the most reliable method as it is based on the energy balance incorporating physiological and aerodynamic parameters without any local calibration under all types of climatic conditions [2,9]. However, the FAO-56 PM method entails the availability of a complete, continuous suite of weather data including solar radiation, wind speed, air temperature, and relative humidity. However, these variables are often unavailable in data-limited countries where meteorological parameters are hard to obtain or are available only in the form of useless short-time series that differ among stations by periods of data collection. Some countries do not have a uniform distribution of full-suite weather sites or lack public access to these data, hindering large-scale and long-term agro-hydrological studies. However, long-term air temperature data are primarily available in spatially dense weather networks across Mongolia.

Daily ET₀ is converted into biome-specific potential evapotranspiration (ET_p), which refers to the evapotranspiration demand from a grassland biome (e.g., steppe grassland in Mongolia) under optimum soil water conditions [10]. This conversion entails the knowledge of the time-variant crop coefficient, K_c, which is well-documented for vegetables, cereals, forages, and fruit trees [2]. However, to our knowledge, a K_c representing vegetation properties under natural vegetation conditions in Mongolia is currently unavailable in the body of literature [11,12,13]. Obtaining this coefficient will allow one to estimate ET_p at daily time steps. This approach is more efficient than inferring values from images of remote sensing data only as noted by [14], who studied ET₀ from the north China regions bordering with Mongolia.

According to [15], the normalized difference vegetation index (NDVI) shows strong positive correlations with evapotranspiration over the majority of grassland areas except for the region near the Gobi Desert [16]. Significant difference occurs between ET₀ and ET_a in this biome. Hence, the regular K_c taken from FAO guidelines is not appropriate in the arid, sparsely vegetated Gobi Desert areas. Research from Inner Mongolia (China) supports this assumption [13]. Therefore, one may adapt a time-variant crop coefficient, K_{c adj} to steppe grasslands in Mongolia depending on satellite-derived leaf area index (LAI) in the steppe region (K_{c adjS})and solar net radiation in the Gobi Desert (K_{c adjD}). Net solar radiation can be estimated from easily accessible weather data, while monthly maps of leaf area index can be retrieved from remote sensing products.

To address this ET_p knowledge gap in Mongolia, we propose a two-fold approach. The first objective is to select a suitable temperature method to estimate daily ET₀ values under data paucity constraints. A limited number of sites with full-suite weather data may be used to evaluate estimates of ET₀. The second objective is to develop a new time-variant crop coefficient (K_{c adj}) to convert ET₀ into ET_p in Mongolian biomes. The mean annual ET_p obtained using this approach could be compared to that obtained by FAO-56 guidelines for forages (not steppe) based on tabulated K_c values in locations across Mongolia.

Ultimately, these estimates of ET_p will be used as crucial input data for ground water recharge models which will be presented in future work.

2. Materials and Methods

2.1. Environmental Settings and Data Availability

Mongolia is a landlocked territory covering about 1.6 million km², located in the heart of the Asian continent. Mongolia has borders with the Russian Federation in the north (3543 km long) and China in the south (4709 km) [17]. Mongolia lies on a high plateau surrounded by mountain ridges in the transition zone between the Siberian taiga and the dry steppes and semi-deserts of central Asia. The country has a dry subarctic continental climate with long cold winters and short hot summers.

The average number of rainy days per year is 105–115. Annual average precipitation (P) is generally low decreasing from the north (350–500 mm) to the south (less than 50 mm) [17]. Maximum (almost 85%) seasonal P occurs in summer [8]. The average annual temperature ranges from −8 °C to +2 °C and is negative from October to March in most parts of the country [17].

In this territory, 80% is pasture-land, 10% forest, 1% farmland, and 9% other types of land. Steppe vegetation is the most common in Mongolia and occupies about 83% of the territory [18]. It lies mainly in the central part of the country, the transitional zone bordering the Gobi Desert to the south, and mountain taiga to the north. The steppe ecosystems are associated with the semi-arid and arid continental temperate climates of the region and are ecologically fragile and sensitive to climate change and anthropogenic disturbances [19]. Perennial plants (50–90%) dominate the Mongolian steppe. The highest percentage of perennial plants occurs in the high-cold steppe. In contrast, the percentage of shrub, dwarf shrub, biennials, and annuals is minimum in the high-cold steppe and gradually increases in the desert steppe [18]. About half of the Mongolian territory is mountainous with an average elevation of 1580 m a.s.l.; about 81% of its territory is above 1000 m and 19% below 1000 m [17]. These mountains are divided into cool and dry types according to their formation of vertical vegetation range. Khentii, Khuvsgul, northwestern Mongolian Altai, Northern Khangai, and Khyangan are referred to as cool type mountains and comprise steppe vegetation. Southern Altai, Gobi Altai, Gobi, and Zuungar mountains are referred to as dry type with desert vegetation and high-cold steppe [18].

We identified a total of 41 locations relatively uniformly distributed across Mongolia with available weather data (Figure 1). We specified that ten weather stations (blue triangles in Figure 1) had a complete set of weather data, while the remaining 31 stations (black triangles) provided only T and P data. The study locations were chosen considering the density, physical geography, latitude and altitude, land use, climate class, and data availability.

The complete data set belonging to the ten weather stations will be exploited for estimating daily ET₀ with the FAO-56 PM equation and temperature-based equations (Section 2.2.).

Table 1. Information (time-period, location, and reference) of data sources.

Collected Data/Parameters	Unit	Period of Data Availability	Source	References
Daily P	mm	2007–2011	NAMEM	[21]
Daily max T, min T, mean T	(°C)	2001–2020	NOAA National Centers for Environmental Information	[22]
LAI	(-)	1981–2015	ORNL DAAC	[23]

shows information on data sources used in this study for all 41 study locations.

Daily P data were retrieved from the National Agency of Meteorology and Environmental Monitoring (NAMEM) [21]. T data at Khatgal weather station were validated with those obtained from the National Oceanic and Atmospheric Administration (NOAA) website [22]. This comparison shows high correlation between remote-sensing and ground-truthing data (available in Figure S1 in Supplemental Materials). Since the ground-based leaf area index (LAI) measurements are highly variable in space and time, the estimates from the remotely sensed products were assumed valid and reliable and were not validated with ground-truth measurements [24]. The LAI monthly mean values were obtained from the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL DAAC) website [23] providing a global 0.25° × 0.25° gridded monthly mean LAI over the period from August 1981 to August 2015. The data were derived from the Advanced Very High-Resolution Radiometer (AVHRR) Global Inventory Modeling and Mapping Studies (GIMMS), and the bi-weekly LAI values were averaged for every month (Figure S2 in Supplemental Materials). Due to the low vegetation cover, the LAI in some parts of the Gobi Desert is unavailable. The inverse distance weighted interpolation tool was used in ArcGIS software (Esri, West Redlands, CA, USA) to estimate the weighted average of the LAI values in the neighborhood of each processing cell. As it follows from the name, this method uses the inverse distance to each point when assigning weights. The monthly average values of LAI extracted from the map at study locations are available (Figure S3 in Supplemental Materials).

2.2. Prediction of Reference Evapotranspiration, ET₀, and Biome-Specific Potential Evapotranspiration, ET_p

We considered two well-known limited-data-requirement equations to predict ET₀, namely, Hargreaves (Har) [25] and Thornthwaite (Tho) [26,27]. We evaluated the prediction performance of Har and Tho equations by comparing these two methods with the FAO-56 PM equation by using a complete meteorological dataset at 10 weather stations [28,29,30] and selected the best performing temperature method to estimate ET₀ (Figure 2a).

The equations are reported in

Table 2. FAO-56 PM, Har and Tho equations with required input data to calculate daily ET₀.

The Methods	Minimum Meteorological Data Requirements						Equations
	Mean T	Max T	Min T	Relative Humidity	Wind Speed	Ra or Rn
FAO-56 PM	+	+	+	+	+	+	$E{T}_0=\frac{0.408∆\left(R_n-G\right)+\gamma \frac{900}{T+273}{u}_2\left(e_s-e_a\right)}{∆+\gamma \left(1+0.34u_2\right)}$
Hargreaves	+	+	+			+	$E{T}_0=0.0023\left(T_m+17.8\right){\left(T_{max}-T_{min}\right)}^{0.5}\left(0.408R_a\right)$
Thornthwaite modified	+						$E{T}_0=\{\begin{array}{c}0, T<0°\\ 0.553{\left(\frac{10T}{I}\right)}^a, 0\le T\le 26.5°\\ \left(-13.86+1.075T-0.0144T^2\right)\frac{h}{12},T\ge 26.5°\end{array}$ $I={\displaystyle \sum }_1^{12}{\left(\frac{T_m}{5}\right)}^{1.514}$ $\alpha =\left(6.75\times {10}^{-7}{I}^3\right)-\left(7.71\times {10}^{-5}{I}^2\right)+(1.79\times {10}^{-2}I)+0.492$

, and we briefly report necessary input data for each equation. In the FAO-56 PM equation, R_n is net radiation at plant surface (MJ m⁻² d⁻¹), G is the soil heat flux density (MJ m⁻² d⁻¹), T is air temperature (°C), u₂ is the wind speed at 2 m height above ground (m s⁻¹), e_s and e_a are saturated and actual vapor pressures (kPa), Δ is the slope of the vapor pressure curve (kPa °C⁻¹), and γ is the psychometric constant (kPa °C⁻¹). Net radiation is usually indirectly measured by a pyranometer. If a weather station lacks pyranometer data, R_n can be estimated from the actual daily duration of bright sunshine (hours per day) [2]. The term G is computed as a fraction of R_n, as suggested by [2] for the reference crop. In the Har equation, R_a is the extraterrestrial radiation expressed in mm d⁻¹ (obtained by multiplying MJ m⁻² d⁻¹ by 0.408), T_m (°C), T_min (°C), and T_max (°C) represent mean, minimum, and maximum temperature, respectively. In the Tho equation, the value I represents the annual heat index, T_m represents i-th month mean air temperature (°C), and h depicts hours of sunlight (hours).

The daily maximum, minimum, mean temperature, relative humidity, and wind speed data were obtained from NAMEM [21]. The hours of sunlight data were downloaded at the nearest available station [31]. The terms R_a and R_n were indirectly estimated from the guidelines on missing climatic data from the FAO-56 report [2].

The FAO-based aridity index (AI) is computed as the ratio between mean annual P and ET₀ [32] and will be used in our study. This index can be considered a proper indicator for climate classification in Mongolia.

After selecting the best temperature model, daily ET₀ was calculated in all 41 study locations with easily accessible data. The crop coefficient considers plant characteristics, such as height, leaf area index, and leaf and stomata properties in order to convert the reference grass ET₀ into ET_p. These plant characteristics indeed influence the aerodynamic resistance, the albedo of crop-soil surface, and canopy resistance. The FAO-56 guidelines report [2] tabulated K_c values for crops, vegetables, forages, and fruit trees referring to a sub-humid climate with an average daytime minimum relative humidity of about 45% and with wind speeds averaging 2 m s⁻¹. These tabulated K_c values under the abovementioned climatic conditions are not present in Mongolia. A study carried out in neighboring parts of Inner Mongolia [12] across the border demonstrates that a developed K_c for steppe in the arid and semi-arid zone is lower than the available K_c value (grazing pasture) taken from the FAO-56 guidelines [2]. The natural vegetation conditions in those climate zones have not been studied in-depth, unlike agricultural crops. Permanent monitoring stations are absent, and the exact vegetation condition in those arid, semi-arid areas is mostly unknown. Therefore, the use of guidelines to develop K_c from FAO-56 report [2] is fraught with uncertainties.

Nevertheless, the natural zones can be grouped into land cover zones of the Gobi Desert and the steppe (

Table A1. Categorization of natural zones.

ID.	Stations	Natural Zone	ID.	Stations	Natural Zone
1	Sukhbaatar	Steppe	22	Baynuul	steppe
2	Tseterleg	Steppe	23	Galuut	steppe
3	Bulgan Mg	Steppe	24	Ulaangom	steppe
4	Khatgal	Steppe	25	Arvaikheer	steppe
5	Tosontsengel	Steppe	26	Choir	steppe
6	Binder	Steppe	27	Mandalgobi	steppe
7	Rinchinlhumbe	Steppe	28	Altai	steppe
8	Khalkh gol	Steppe	29	Khoriult	steppe
9	Erdenemandal	Steppe	30	Hovd	Gobi Desert
10	Baruunkharaa	Steppe	31	Ulgii	Gobi Desert
11	Baruunturuun	Steppe	32	Ekhiingol	Gobi Desert
12	Erdenetsagaan	Steppe	33	Gurvantes	Gobi Desert
13	Chingis khaan (UB)	Steppe	34	Tooroi	Gobi Desert
14	Choibalsan	Steppe	35	Sainshand	Gobi Desert
15	Undurkhaan	Steppe	36	Khanbogd	Gobi Desert
16	Matad	Steppe	37	Zamiin Uud	Gobi Desert
17	Murun	Steppe	38	Baitag	Gobi Desert
18	Uliastai	Steppe	39	Dalanzadgad	Gobi Desert
19	Baruun-Urt	Steppe	40	Saikhan-Ovoo	Gobi Desert
20	Erdenesant	Steppe	41	Tsogt-Ovoo	Gobi Desert
21	Dariganga	Steppe

in Appendix A). Then, different methods to develop K_c based on different climate and phenological characteristics for those two zones were explored and implemented in our study (Figure 2b). Previous studies have indicated that the K_c values vary significantly during the growing season; therefore, it is impossible to assume K_c as constant over time. This study attempts to propose a time-variant crop coefficient, K_{c adj}, using easily-retrievable data, such as solar radiation or LAI, and therefore, ET_p values can be obtained (ET_p = ET₀ × K_{c adj}) in study locations.

In the Gobi Desert ecosystem, the crop coefficient taken from the FAO-56 guidelines [2] is not suitable due to scarce and sparse vegetation. The following simple relation is, therefore, used to estimate daily variations of the proposed crop coefficient [12], K_{c adjD}, based on the measurement of solar radiation:

$$K_{c adjD}=0.02\ast R_n$$

(1)

where R_n is net solar radiation.

In the steppe zone in Mongolia, similar studies are scarce, and there are no readily available approaches providing crop coefficients in the FAO-56 report [2]. Some guidelines for (non-crop) grassland in arid climates require parameters such as vegetation height, air relative humidity, and wind speed, and their use is not straightforward. For example, the crop coefficient, K_c,p, in a non-irrigated pasture site in Florida, USA [33] ranged from 0.47 to 0.92 and could be presented by a linear function of leaf area index (LAI):

$$K_{c,p}=aLAI+b$$

(2)

where the empirical parameters are assumed as a = 0.330 and b = 0.451. However, the natural vegetation growth is subject to various constraints. Therefore, we propose to adapt the crop coefficient to steppe grassland (K_{c adjS}) proposed by [2] for sparse vegetation under local conditions:

$$K_{c adjS}=K_{c,p }-A_{cm}$$

(3)

where A_cm is another empirical parameter given by the following equation:

$$A_{cm}=1-{\left[\frac{LAI}{LA{I}_{dense}}\right]}^{0.5}$$

(4)

where LAI_dense is the LAI expected for the same crop under normal, standard crop management practices. The LAI_dense can be predicted from the ground cover ratio.

The same linear function could not be applied in all study locations throughout the steppe due to contrasting vegetation characteristics. After multiple attempts, the LAI_dense values in the steppe zone in study locations with higher-than-average LAI values (LAI > 0.6) and locations with lower-than-average values (LAI < 0.6) were calculated using the following equations:

$$LA{I}_{dense}=\{\begin{array}{cc}\hfill \frac{0.95-0.2}{0.6-0}LAI+0.2,& LAI<0.6\hfill \\ \hfill \frac{3.03-0.95}{2.53-0.6}\left(LAI-0.6\right)+0.95,& LAI>0.6\hfill \end{array}$$

(5)

Figure 3 shows A_cm and LAI_dense as a function of LAI.

By estimating LAI_dense from Equation (5), daily K_{c adjS} and A_cm can be calculated in Equations (3) and (4), respectively, and therefore, ET_p values can be obtained (ET₀ × K_{c adjS}) in study locations belonging to the steppe zone in Mongolia. Grass pasture is assumed to be predominant in the steppe. The growing season of grass pasture is assumed to start seven days before recording 4 °C in spring for the last time until seven days after recording −4 °C in fall for the first time in all study locations. The crop coefficient in the dormant season is considered as 0.1 in all study locations by the guidance of [2].

As indicated above, leaf area index LAI plays a critical role in generating input data for modeling the water balance of the vadose zone. This parameter is used in Beer’s law, which partitions ET_p into potential evaporation, E_p, and potential transpiration, T_p [34]:

$$E_p=E{T}_p{e}^{-kLAI}=E{T}_p\left(1-SCF\right)=E{T}_p{e}^{-0.463LAI}$$

(6)

$$T_p=E{T}_p\left(1-e^{-kLAI}\right)=E{T}_{p}SCF=E{T}_p-E_p$$

(7)

where SCF is the soil cover fraction (–), and k is the radiation extinction constant (–), usually assumed to be equal to 0.463 as indicated by various studies, e.g., [34,35,36].

2.3. Evaluation Criteria

To measure the predictive capability of all prediction methods mentioned above, we selected two statistical performance indicators: the root mean square error (RMSE), which combines both bias and lack of precision, and the coefficient of determination (R²), which measures how well the data pairs fit to a line:

$$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum }_{i=1}^n{\left(o_i-e_i\right)}^2}$$

(8)

$$R^2=\frac{{{\displaystyle \sum }}_{i=1}^n{\left(o_i-e_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(o_i-\overline{o}\right)}^2}$$

(9)

where o_i is the reference value (for example, FAO-56 PM ET₀), $\overline{o}$ is the mean of reference values, and e_i indicates estimated values (for example, ET₀-Har and ET₀-Tho). Subscript i is the index of data in series (or day number), and n is the total number of days. Daily values of ET₀ and ET_p will also be aggregated at monthly and annual sums; therefore, RMSE units are also expressed as mm month⁻¹ and mm year⁻¹, respectively.

3. Results

3.1. Prediction of Grass-Reference Evapotranspiration, ET₀

The relationship between meteorological variables and FAO-56 PM daily ET₀ for 10 weather stations is expressed in terms of Pearson correlation coefficients presented in

Table 3. Pearson correlation coefficients between FAO-56 PM daily ET₀ and meteorological variables over the 10 weather stations in Mongolia.

	Wind Speed	Relative Humidity	Air Temperature	Net Radiation	Sunshine Hours
1. Galuut	0.51	−0.57	0.91	0.92	0.74
2. Tsetserleg	0.16	−0.23	0.91	0.91	0.84
3. Bulgan	0.30	−0.47	0.90	0.92	0.75
4. Khovd	0.58	−0.76	0.90	0.92	0.84
5. Erdenetsagaan	−0.02	−0.63	0.91	0.88	0.69
6. Choibalsan	0.04	−0.69	0.91	0.91	0.83
7. Khatgal	0.01	−0.28	0.90	0.92	0.85
8. Baruunurt	0.20	−0.72	0.91	0.90	0.71
9. Undurkhaan	0.20	−0.73	0.90	0.90	0.72
10. Tsogtovoo	0.21	−0.68	0.91	0.91	0.84

.

High positive correlation coefficients are observed between ET₀ and air temperature and net radiation, while negative correlation coefficients are reported when relating ET₀ to the relative humidity. The results agree with the conclusion of [37] that the net radiation and air temperature are the most important controlling factors on ET₀. This proves the potential of temperature-based ET₀ models in Mongolia.

When considering estimates of daily ET₀ values, the comparison between Har and FAO-56 PM equations (blue line in Figure 4) leads to a minimum RMSE of 0.56 mm d⁻¹ (R² = 0.93) in Khatgal and a maximum RMSE of 1.44 mm d⁻¹ (R² = 0.87) in Tsogtovoo. The comparison between Tho and FAO-56 PM equations (red line in Figure 4) spans between RMSE of 0.76 mm d⁻¹ (R² = 0.88) in Bulgan and RMSE of 1.74 mm d⁻¹ (R² = 0.85) in Tsogtovoo. The Har ET₀ method shows lower RMSE and higher R² than those obtained from the Tho equation over the 10 test locations. The comparison between FAO-56 PM-based and temperature-based equations for predicting daily values of ET₀ at Khatgal and Tsogtovoo weather stations are presented in Figure S4 in Supplemental Materials.

A temperature-based model ignores the importance of meteorological variables such as relative humidity, solar radiation, and vapor pressure deficit, as diagnosed by high correlation coefficients listed in Table 3. The FAO-56 PM-based monthly cumulative ET₀ also better matches with the Har method, as can be seen in Figure S5 in Supplemental Materials. One of the drawbacks of the Tho method is that ET₀ can not be calculated in the winter months when the temperature drops below 0 °C. Therefore, according to the cumulative results, the Tho method systematically underestimates the reference ET₀ estimated by the FAO-56 PM equation.

The mean annual ET₀ sums predicted by the three methods are visualized in Figure 5. The FAO-56 PM-based predictions of mean annual ET₀ sums are in accordance with the estimates in Inner Mongolia (China) reported by [38]. ET₀, predicted by the Har and Tho equations, consistently suffers from underestimation. RMSE is 159.3 mm y⁻¹ and 248.3 mm y⁻¹ for Har and Tho equation, respectively.

As seen from the statistical results and cumulative comparisons, the Har outperforms the Tho equation for estimating ET₀. We concur with [39] that lack of local calibration might be unacceptable for practical applications. We are also aware that [40] observed that the Har equation generates a significant bias in northeastern China. However, we are forced to use the uncalibrated Har ET₀ method due to the chronic data paucity in Mongolia. Therefore, we selected the Har equation over the 41 study locations to predict ET₀, which will be converted into ET_p in Section 3.2. Annual sums of Har-ET₀ are presented in

Table A2. Annual sums of ET₀ over the 41 weather stations in Mongolia.

ID.	Stations	Annual Har ET0 (mm)					Mean Har ET0 (mm)	CV (%)
		2007	2008	2009	2010	2011
1	Sukhbaatar	861	847	929	812	812	852	5.6
2	Tseterleg	845	819	801	763	769	799	4.3
3	Bulgan Mg	891	854	854	835	782	843	4.7
4	Khatgal	742	715	694	691	695	707	3
5	Tosontsengel	791	762	753	696	729	746	4.8
6	Binder	907	818	823	793	840	836	5.1
7	Rinchinlhumbe	723	686	663	666	687	685	3.5
8	Khalkh gol	910	872	834	863	839	863	3.5
9	Erdenemandal	871	836	810	793	789	820	4.2
10	Baruunkharaa	921	889	884	846	849	878	3.5
11	Baruunturuun	792	769	727	713	749	750	4.2
12	Erdenetsagaan	926	848	847	849	820	858	4.7
13	Chingis khaan (UB)	584	561	571	757	694	634	13.8
14	Choibalsan	952	881	876	860	880	890	4
15	Undurkhaan	987	914	883	874	894	910	5
16	Matad	976	882	882	877	854	894	5.3
17	Murun	865	834	814	777	798	817	4.1
18	Uliastai	842	818	790	755	772	795	4.4
19	Baruun-Urt	972	896	900	880	862	902	4.6
20	Erdenesant	881	843	804	772	750	810	6.5
21	Dariganga	835	841	819	864	866	845	2.4
22	Baynuul	819	770	741	714	735	756	5.4
23	Galuut	769	797	763	739	708	755	4.4
24	Ulaangom	863	846	798	790	819	823	3.8
25	Arvaikheer	830	808	825	780	776	804	3.1
26	Choir	954	893	898	857	839	888	5
27	MandalGobi	954	915	922	861	871	905	4.2
28	Altai	778	753	740	691	706	733	4.8
29	Khoriult	987	982	1001	955	952	975	2.2
30	Hovd	902	898	867	824	846	867	3.9
31	Ulgii	846	838	781	777	808	810	3.9
32	Ekhiingol	1121	1139	1159	1106	1118	1129	1.8
33	Gurvantes	886	891	921	869	871	888	2.4
34	Tooroi	1104	1130	1121	1039	1038	1086	4.1
35	Sainshand	1029	1000	1012	984	952	996	2.9
36	Khanbogd	1034	995	1029	971	983	1002	2.8
37	Zamiin Uud	1033	1010	1041	1002	1010	1019	1.7
38	Baitag	1000	1006	957	886	964	962	5
39	Dalanzadgad	985	985	1012	964	960	981	2.1
40	Saikhan-Ovoo	981	957	1003	946	926	963	3.1
41	Tsogt-Ovoo	1015	985	1012	955	936	981	3.5
Spatial-average ET0		902	873	867	840	843

in Appendix A. The ET₀ annual sums broadly varied in space with low temporal variability in each station through 5 years (2007–2011). The coefficient of variation (CV) was lower than 10% in 40 out of 41 stations. If we consider the spatial-average ET₀ in each year, 2007 and 2011 had the highest and lowest values, respectively.

Finally, we carried out a second validation of the Har ET₀ predictions. A global map of monthly ET₀ estimated with FAO-56 PM referring to the period 1961–1990 [41] was used to aggregate the mean annual ET₀ (Figure 6) and extract corresponding values over the 41 weather stations.

ET₀ values tend to increase towards the south in general. The lowest mean annual ET₀ value is 634 mm, while the highest is 1129 mm. The Har ET₀ values are compared to the corresponding FAO-56 PM ET₀ by obtaining RMSE = 93 mm y⁻¹ and R² = 0.69. Nevertheless, the Har-based ET₀ results look consistent with [41] and previous studies carried out in Mongolia [8,25,42] and Inner Mongolia [14] and appear to form a reliable basis for further processing and modeling.

3.2. Prediction of Biome-Specific Potential Evapotranspiration, ET_p

The ET_p is calculated by multiplying ET₀ with the time-variant K_{c adj} in the Gobi Desert (K_{c adjD}) and in the steppe grasslands (K_{c adjS}), as described beforehand. By assuming the reliability of Har ET₀ predictions, our attention is now focused on the assessment of crop coefficient, K_{c adj} in Mongolia, and its impact on the prediction of ET_p. To this end, we considered six weather stations in the steppe region (Sukhbaatar, Tosontsengel, Baruunkharaa, Undurkhaan, Erdenesant, Arvaikheer) and one representative weather station in the Gobi Desert (Saikhanovoo) (Figure S6 in Supplemental Materials) where we predicted ET_p by using the developed K_{c adj} for natural vegetation (Figure 7b) or the tabulated K_c (Figure S7 in Supplemental Material) based on grazing pasture in the FAO-56 guidelines (see Table 17 in [2]). Our developed crop coefficient, K_{c adj}, depends on LAI (Figure 7a) retrieved from remote-sensing monthly maps in the grassland steppe (K_{c adjS}) or on solar radiation in the Gobi Desert (K_{c adjD}). We observed a decrease in LAI (Figure S2 in Supplemental Materials) and K_{c adjS} towards the south, where conditions become arid. The use of time-variant LAI has the advantage of generating time-variant K_{c adjS} according to our methodology. In contrast, tabulated values in the FAO-56 report provide constant K_c values in three growing season phases.

The developed (K_{c adj}) and tabulated K_c values are used to convert ET₀ into biome-specific ET_p. Figure 8 shows an illustrative example by comparing predictions of ET_p at three stations (Sukhbaatar, Arvaikheer and Saikhanovoo) with contrasting vegetation cover. K_{c adjS} is used at Sukhbaatar and Arvaikheer (steppe region) while K_{c adjD} is used at Saikhanovoo (Gobi Desert). The prediction of ET_p with both K_{c adj} and tabulated K_c values was similar over the first weather station (Sukhbaatar), with vegetation cover characterized by LAI > 1 and K_{c adjS} > 0.6 during the growing season in summer (green circles in Figure 7). Nevertheless, vegetation cover halved at the second weather station (Arvaikheer) or reduced to almost zero at the third weather station in the Gobi Desert (Saikhanovoo) in terms of LAI and K_{c adj} (Figure 7). The impact of the developed K_{c adj} value on the ET_p prediction can be visualized in Figure 8. The tabulated K_c values (red circles in Figure 8a–c) generated similar predictions of ET_p over the three stations despite the contrast in vegetation cover. On the other hand, the impact of the scarce vegetation cover on the developed K_{c adj} value over Arvaikheer and especially Saikhanovoo in the Gobi Desert induced a drastic reduction in ET_p (blue circles in Figure 8a–c). The comparison between ET_p predictions based on tabulated K_c and ET_p predictions based on developed K_{c adj} is shown in Figure 8d–f. Despite high R² values diagnosing similar temporal trends in response to seasonal temperature change, we report consistent bias over the weather station at Arvaikheer (RMSE = 1.69 mm d⁻¹, Figure 8e) and Saikhanovoo (RMSE = 2.65 mm d⁻¹, Figure 8f) in the Gobi Desert.

In contrast, both tabulated and developed K_{c adjS} at the weather station of Sukhbaatar led to a similar prediction of ET_p (Figure 8d) as diagnosed by a very low RMSE (RMSE = 0.40 mm d⁻¹).

The mean annual sums of ET_p based on tabulated (orange bars) and developed (blue bars) K_c over the seven weather stations are displayed in Figure 9 with increasing discrepancy under scarce vegetation cover conditions, characterized by a gradient from north to south. Very low differences of 52.6 mm and 140.5 mm are shown at Sukhbaatar and Tosontsengel, respectively. The highest differences were reported in the following four stations with 298.8 mm, 385.2 mm, 365.7 mm, and 407.4 mm at Baruunkharaa, Undurkhaan, Erdenesant, and Arvaikheer, respectively. The highest difference of 674.3 mm was reported at Saikhanovoo in the Gobi Desert.

Mean annual sums of P, ET₀, ET_p (based on our developed K_c), T_p, and E_p and corresponding aridity index, AI, over the 41 study locations in Mongolia are presented in

Table A3. Mean annual sums of water fluxes over 41 weather stations in Mongolia.

ID.	Stations	P (mm)	ET0 (mm)	ETp (mm)	Ep (mm)	Tp (mm)	AI	Class
1	Sukhbaatar	277	852	695	329	366	0.32	Semi-arid
2	Tseterleg	323	799	615	270	344	0.4	Semi-arid
3	Bulgan Mg	287	843	448	284	164	0.34	Semi-arid
4	Khatgal	277	707	449	245	204	0.39	Semi-arid
5	Tosontsengel	193	746	501	271	230	0.26	Semi-arid
6	Binder	301	836	521	297	224	0.36	Semi-arid
7	Rinchinlhumbe	193	685	428	243	185	0.28	Semi-arid
8	Khalkh gol	291	863	489	299	190	0.34	Semi-arid
9	Erdenemandal	254	820	423	269	154	0.31	Semi-arid
10	Baruunkharaa	316	878	460	298	162	0.36	Semi-arid
11	Baruunturuun	210	750	400	266	135	0.28	Semi-arid
12	Erdenetsagaan	207	858	353	233	120	0.24	Semi-arid
13	Chingis khaan (UB)	244	634	293	207	86	0.39	Semi-arid
14	Choibalsan	205	890	305	197	108	0.23	Semi-arid
15	Undurkhaan	238	910	389	291	98	0.26	Semi-arid
16	Matad	211	849	362	267	95	0.25	Semi-arid
17	Murun	227	755	323	232	90	0.3	Semi-arid
18	Uliastai	188	795	338	247	91	0.24	Semi-arid
19	Baruun-Urt	172	902	359	270	88	0.19	Arid
20	Erdenesant	246	810	308	237	71	0.3	Semi-arid
21	Dariganga	145	845	305	239	66	0.17	Arid
22	Baynuul	190	756	290	225	65	0.25	Semi-arid
23	Galuut	193	755	244	196	47	0.26	Semi-arid
24	Ulaangom	109	823	271	223	48	0.13	Arid
25	Arvaikheer	219	804	228	187	41	0.27	Semi-arid
26	Choir	111	888	237	200	38	0.12	Arid
27	MandalGobi	93	731	188	161	26	0.13	Arid
28	Altai	156	733	173	150	23	0.21	Semi-arid
29	Khoriult	95	975	247	212	35	0.1	Arid
30	Khovd	119	867	242	210	32	0.14	Arid
31	Ulgii	95	810	126	108	18	0.12	Arid
32	Ekhiingol	57	1129	159	139	20	0.05	Arid
33	Gurvantes	100	888	162	141	21	0.11	Arid
34	Tooroi	60	1086	157	137	21	0.05	Arid
35	Sainshand	109	996	148	133	16	0.11	Arid
36	Khanbogd	115	1002	174	156	18	0.11	Arid
37	Zamiin Uud	93	1019	154	138	16	0.09	Arid
38	Baitag	93	962	145	131	14	0.1	Arid
39	Dalanzadgad	128	981	176	161	15	0.13	Arid
40	Saikhan-Ovoo	113	963	147	134	13	0.12	Arid
41	Tsogt-Ovoo	79	981	239	218	21	0.08	Arid

in Appendix A.

We observe the consistent reduction of ET₀ into ET_p in accordance with the study presented by [13] in arid and semi-arid classes. The difference between ET₀ and ET_p increases over the Gobi Desert region, where the K_{c adj} values decrease consistently.

The aridity increases to the south with mean annual temperature increase, and precipitation decrease (Figure S8 in Supplemental Materials). Therefore, the effect from mountain ranges also can be perceived, especially in the south part of Mongol-Altai and Gobi-Altai mountain ranges. The ratio of ET₀ to P varies from 3 to 12 times in study locations, while the ratio ET_p to P is about 2.5 to 3 times. E_p constitutes a large portion of ET_p with low LAI in the southern Gobi Desert locations (Figure S9 in Supplemental Materials). In contrast, in northern Mongolia, T_p importance increases, as seen from Table A3. Especially in the Gobi Desert region, E_p constitutes more than 86% of ET_p over the study locations. The variations in T_p closely follow the variation in LAI. All study locations in Mongolia are categorized into the arid macro-class, and AI ranges from 0.05 to 0.40. According to Table A3, climate classes belong to arid to semi-arid classes in study locations. ET₀ values are high in the Gobi Desert region due to the high mean temperatures. On the other hand, the ET_p values consistently decrease in the Gobi Desert Region due to very low LAI values characterizing scarce vegetation cover as depicted by very low daily K_{c adjD} values in the Gobi Desert in Figure 10a. The difference between mean annual ET₀ and ET_p gets higher in the Gobi Desert and closer in the steppe (Figure S10 in Supplemental Materials).

The relation between climate aridity (in terms of AI) and the ratio of mean annual ET_p to mean annual ET₀ (or ET_p/ET₀) is shown in Figure 10b. Data are grouped according to the land cover class (Gobi Desert and steppe) and climate class (vertical dashed line delimits arid and semi-arid climate classes, respectively). The locations belonging to the Gobi Desert (yellow circles) cluster very closely in the arid class, while the steppe points are scattered mostly in the semi-arid climate. The fit of the linear regression shows an acceptable R² value and describes more than 80% reduction of ET₀ in the Gobi Desert and about 54% reduction in the steppe locations under semi-arid conditions.

4. Discussion

The first goal of this study was to find a suitable temperature-based method to reliably estimate ET₀ in Mongolia [6]. We compared the Hargreaves (Har) and Thornthwaite (Tho) equations with the Penman–Monteith (FAO-56 PM) equation. The latter is highly recommended by the International Commission for Irrigation Drainage, Food and Agriculture Organization of the United Nations and ASCE-Evapotranspiration in Irrigation and Hydrology Committee [43,44]. Both Har-based and Tho-based models mostly underestimate FAO-56 PM-based average annual ET₀ in most weather stations in arid and semi-arid conditions, as reported by previous studies [38,45]. The underestimation is observed in other studies evaluating the Har model in arid and semi-arid conditions in several parts of the world [46,47,48,49]. In this study, we propose to select the Har method, which outperforms the Tho equation to predict daily ET₀. A comparison between FAO-56 PM and Har equations for predicting ET₀ has been carried out all over the world. Similar RMSE values between FAO-56 PM and the uncalibrated Har equation reported in Mongolia have also been observed in southern Italy [50], in south-east Spain [51], in the U.S. High Plains [39], and northwest China [52], while lower RMSE values are reported in arid and semi-arid areas in China [53]. The Har ET₀ estimates can be considered acceptable as reported in some studies carried out in Mongolia [8,19,42].

The second goal of this study is the assessment of the biome-specific potential evapotranspiration, ET_p, in Mongolia. The key step is to find a suitable method to describe the crop coefficient, K_c, to convert ET₀ into ET_p. The FAO-56 guidelines recommend the calculation of K_c in each crop growing phase. Larger-than-normal crop coefficient values should be attributed to a well-watered crop under arid and semi-arid climate conditions. It is expected that K_c should be larger under arid conditions when the agricultural crop has leaf area and roughness height greater than that of the reference grass. However, this is not the case in Mongolia. K_c values in Mongolia are currently unavailable in any type of natural vegetation. Very few studies have been conducted in semi-arid natural environments [13].

Even though two different methods were used to develop K_{c adj}-values depending on the biome (LAI-dependent K_{c adjS} in steppe, R_n-dependent K_{c adjD} in the Gobi Desert), the results have a smooth transition in K_{c adj}-values in the study locations. The K_{c adjD} estimates in the Gobi Desert region are similar to the results presented by [12,13] in Inner Mongolia. In well-managed cropland, the standard conditions are generally the actual field conditions. The ET_p is partitioned in potential evaporation and potential transpiration using available maps of LAI in Mongolia. The E_p constitutes a major part of ET_p with low LAI in the southern Gobi Desert locations, while T_p increases toward the northern region. According to [12,13], daily K_c values in the growing season ranged from 0.02 to 0.50 with an average value of 0.17 and 0.15 to 0.17 in a temperate desert in Inner Mongolia. Both studies were performed in the Gobi Desert (Inner Mongolia).

We observe that using tabulated K_c values in northern Mongolia is acceptable, while under sparse vegetation cover conditions (in central and southern Mongolia), we highly recommend to relate crop coefficient to easily-retrievable LAI (remote sensing maps) in the steppe region or to solar radiation in the Gobi Desert region. A proper prediction of ET_p is key to obtain successful model simulations. The impact of ET_p prediction on GR simulations will be treated in a follow-up study.

5. Conclusions

This study evaluates a protocol for estimating the ET_p in Mongolia under limited data availability. The majority of the auxiliary data required for this study have been collected from remote-sensing products and local ground-based measurements of meteorological data. This practice can be helpful under data paucity constraints in many areas with an arid/semi-arid climate.

It is necessary to reliably estimate ET₀ based on temperature data in Mongolia. Despite some underestimation bias, we recommend the temperature-based Hargreaves equation that reliably predicts ET₀, as verified by comparison with FAO-56 PM results.

It is also necessary to assess the crop coefficient, K_c, to convert ET₀ into ET_p. In this study, we introduce a modified time-variant crop coefficient, K_{c adj}, specific for the two main biomes in Mongolia, namely, the Gobi Desert (K_{c adjD}) and the steppe grasslands (K_{c adjS}). The K_c values tabulated in the FAO guidelines generate spatially uniform predictions of ET_p over the 41 experimental locations characterized by contrasting vegetation cover. In contrast, the developed K_{c adj} value induces a drastic reduction in ET_p towards the arid zone. We, therefore, recommend using LAI-dependent K_{c adjS}-values in the steppe and radiation-dependent K_{c adjD}-values in the Gobi Desert zone. Approximately 80% and 54% reduction of ET₀ into ET_p is reported in the Gobi Desert and in the steppe locations, respectively.

Model performance can be improved by increasing data availability and quality. On the one hand, the Hargreaves equation would benefit from long time series (in the order of decades) of air temperature to estimate ET₀. On the other hand, the empirical equations describing the adjusted crop coefficient values would be enhanced if based on direct measurements over representative hotspots in Gobi Desert and steppe biomes. Results can be used to develop K_{c adj} under natural vegetation conditions in similar areas. This methodology for predicting ET_p can be used in modeling tools of the vadose zone, climate models, and water balance studies with only a few parameters and without labor-demanding field measurements.