Altitude Correction of GCM-Simulated Precipitation Isotopes in a Valley Topography of the Chinese Loess Plateau

Abstract

Altitude is one of the important factors influencing the spatial distribution of precipitation, especially in a complex topography, and simulations of isotope-enabled climate models can be improved by altitude correlation. Here we compiled isotope observations at 12 sites in Lanzhou, and examined the relationship between isotope error and altitude in this valley in the Chinese Loess Plateau using isoGSM2 isotope simulations. Before altitude correction, the performance using the nearest four grid boxes to the target site is better than that using the nearest box; the root mean square error in δ¹⁸O using the nearest four grid boxes averagely decreases by 0.37‰ compared to that using the nearest grid boxes, and correlation coefficient increases by 0.05. The influences of altitude on precipitation isotope errors were examined, and the linear relationship between altitude error and isotope simulations was calculated. The strongest altitude isotopic gradient between δ¹⁸O mean bias error and altitude error is in summer, and the weakest is in winter. The regression relationships were used to correct the simulated isotope composition. After altitude correction, the root mean square error decreases by 1.21‰ or 0.86‰ using the nearest one or four grid boxes, respectively, and the correlation coefficient increases by 0.13 or 0.08, respectively. The differences between methods using the nearest one or four grids are also weakened, and the differences are 0.02‰ for root mean square error and −0.01 for the correlation coefficient. The altitude correction of precipitation isotopes should be considered to downscale the simulations of climate models, especially in complex topography.

1. Introduction

As natural tracers of hydrological circulation, the stable hydrogen and oxygen isotopes in precipitation are sensitive to modern and historical environmental changes [1,2,3]. Isotope fractionations occur when water vapor evaporates, condenses, transports, and mixes, which results in complex spatial patterns and temporal variations of precipitation isotopes [4,5,6]. The global samplings of precipitation isotopes dated back to the mid-20th century, and a number of observations since then provide a useful tool to understand the isotope tracers in the water cycle [7,8,9]. The environmental signals in modern precipitation isotopes on an annual or even longer timescale are also an important basis to reconstruct climate in the past using proxies [10,11,12]. The existing isotope datasets longer than 30 years are still very limited, and the spatial distribution of sampling sites is uneven, which makes it difficult to examine the long-term hydrological and climate controls on precipitation isotopes [13,14].

Isotope-enabled climate models, especially the general circulation models (GCM), are useful to acquire the continuous time series of precipitation isotopes at various time scales [15,16,17]. Due to atmospheric dynamics in the climate models, the isotope-enabled simulation is considered to be an important supplementary to in situ measurements. However, the spatial resolutions of climate models are usually coarse, and many topography-related information is smoothened. The performances of prediction models vary greatly in large spatial scale, with usually good performance in plain areas and poor simulation in complex terrains [18,19], indicating the importance of altitude correction of precipitation isotopes especially in a complex topography with large altitude fluctuation [20,21]. Compared to some global or regional long-term mean products of precipitation isotopes [22,23,24], the climate-model-derived simulation should be improved in spatial resolution, especially in small-scale cases with complex terrain, where altitude correction or downscaling is crucial for climate-model-simulated isotope data.

Usually, the precipitation isotopes negatively correlate with altitude in the mountains, which is also known as the altitude effect [25,26,27]. When the moisture transports along the upwind slope, the vapor condensation is usually associated with temperature and humidity at different altitudes and then causes a decreasing trend in isotope ratios as the altitude rises [28,29,30]. This provides a practical method to downscale or calibrate the climate-model-simulated isotopes. If the relationship between isotope or isotope error and altitude is identified, the knowledge of spatial patterns of precipitation isotopes in mountainous areas can be greatly improved. It should be noted that an isotope observation network with a small spatial domain and complex altitude is needed to establish this quantitative relationship, i.e., multiple sites with large altitude gradients are required to correct the precipitation isotopes using altitude.

Lanzhou is a valley city located at the upper Yellow River in western China, and there have been a number of precipitation isotope studies in past decades. Stable hydrogen and oxygen isotope compositions were analyzed at more than ten sites across this city, which provide a platform to examine the spatial representativity of precipitation isotopes in complex topography. In this study, we used two methods to correct simulated data of the isotope-incorporated global spectral model version 2 (isoGSM2) in Lanzhou, and examined the role of altitude on precipitation isotope simulations. The work aims to provide methods to improve the performance of isotope simulations in a complex topography in a specific location.

2. Materials and Methods

2.1. Study Area

Lanzhou (35°34′ N–37°00′ N, 102°36′ E–104°35′ E) is the capital city of Gansu Province in western China, and the area is approximately 13,100 km² (Figure 1). As a valley city at the upper reaches of the Yellow River, the study area is located in the western part of the Chinese Loess Plateau, and is close to the eastern margin of the Qinghai–Tibet Plateau. The downtown area is distributed along a narrow valley, and the Yellow River goes across from west to east. The altitude of most areas ranges between 1500 and 3000 m a.s.l., and the downtown area is approximately 1500 m a.s.l. Located at the northwestern margin of the summer monsoon, the study area is jointly influenced by the monsoon and westerly moisture sources. Precipitation is mainly concentrated in the summer months.

2.2. Isotope Data

2.2.1. Measured Isotope Data

Here we compiled the stable water isotopes in precipitation observed across the study region in past decades (

Table 1. List of latitude, longitude, altitude, and period of each sampling site.

Site	Latitude (N)	Longitude (E)	Altitude (m)	Sampling Period	Number of Samples
Anning	36°06′	103°44′	1548	2011–2014	191
Gaolan	36°21′	103°56′	1668	2011–2014	260
Daheng	36°40′	103°50′	2029	2013–2014	53
Hezui	36°12′	103°08′	1662	2013–2014	97
Doujiashan	36°12′	103°57′	1725	2013–2014	65
Renshoushan	36°08′	103°41′	1657	2013–2014	79
Yongdeng	36°45′	103°15′	2118	2011–2014	283
Wushengyi	36°53′	103°10′	2297	2013–2014	101
Yuzhong	35°52′	104°09′	1874	2011–2014	225
Gongjing	36°03′	104°23′	2482	2013–2014	78
Lanzhou	36°03′	103°53′	1517	1985–1987, 1996–1999	39
Xiaguanying	36°02′	104°25′	2400	2016–2017	89

). There are 12 sampling sites acquired from three data sources: (1) the city-scale measurements during 2011–2014 [31]. From April 2011 to October 2014, there were four continuous sampling sites (Anning, Yuzhong, Gaolan, and Yongdeng); from October 2013 to October 2014, six additional sites were added (Renshoushan, Doujiashan, Wushengyi, Daheng, Gongjing, and Hezui). Here, the 1432 event-based precipitation samples collected from 2011–2014 were weighted to 196 monthly data using precipitation amounts. (2) The measurements in the Global Network of Isotopes in Precipitation (GNIP) Lanzhou site [32]. There are 39 monthly data of stable water isotopes from 1985–1987 and 1996–1999. (3) Measurements at Xiaguanying from April 2016 to October 2017 [33]. The event-based precipitation samples collected at Xiaguanying are weighted to 16 monthly data. Among the 12 sites, the altitude ranges between 1517 m (Lanzhou) and 2482 m (Gongjing).

2.2.2. Simulated Isotope Data

The precipitation isotopes at a 6 h interval (0:00, 6:00, 12:00, and 18:00 UTC) as well as corresponding surface air pressure from 1979 to 2020 were simulated using isoGSM2 [34]. This stable isotope-enabled general circulation model simulates high-resolution variations in stable isotopes in precipitation and water vapor, which has been applied to examine atmospheric water transport [35,36,37].

The stable oxygen isotope compositions are expressed as a delta notation relative to Vienna Standard Mean Ocean Water (VSMOW) as:

$$\delta {}_{}{}^{18}\mathrm{O}=\left(\frac{q_{{\mathrm{H}}_2^{}{}_{}{}^{18}\mathrm{O}}/q_{{\mathrm{H}}_2\mathrm{O}}}{R_{}}\right)\times 1000‰$$

(1)

where q is the content for water molecule of H₂¹⁸O or H₂O, and R is the isotope ratio of ¹⁸O/¹⁶O.

The precipitation isotope data were weighted to a daily, monthly, or seasonal series using precipitation amount when necessary:

$${\delta }_{\mathrm{w}}=\frac{\sum P_i{\delta }_i}{\sum P_i}$$

(2)

where δ_w is the weighted average isotope value, P_i is the precipitation amount, and δ_i is the original isotope value in precipitation. Seasons are defined as spring (March to May), summer (June to August), autumn (September to November), and winter (December to February).

2.3. Methods

2.3.1. Altitude-Correlation Method

Two methods are used to acquire the simulated precipitation isotopes at the target sites. For method 1, the isotope error and altitude error for each site are calculated using the simulated isotope value minus the observed isotope value. The simulated isotope values and altitude of the target site are replaced by those at the nearest grid box of the isoGSM simulations. The simulated altitude is based on the simulated surface air pressure using the barometric formula. The linear regression using the least square method is then conducted between the altitude error and isotope value error for spring, summer, autumn, and winter. The slope of the linear regression is used to correct the simulated isotope, when the altitude difference between the simulated and observed locations is known.

For method 2, to acquire the simulated isotope values and altitude for each site, the four nearest grid boxes are applied, which is different from method 1 in which only the nearest box is involved. The bilinear interpolation is conducted to synthesize the simulated isotope values and altitude at four locations into one target location. Then the linear regression is also used to correct the simulated isotope values using the altitude difference, which is similar to method 1.

2.3.2. Statistical Measures

Several statistical measures were used to evaluate the simulation, including root mean square error (RMSE), mean absolute error (MAE), mean bias error (MBE), and correlation coefficient (R).

The formula for RMSE is as follows:

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{n}{\sum }_{i=1}^n{(y_i-k_i)}^2}$$

(3)

where y_i is the observed value, k_i is the simulated value, and n is the number of samples. The smaller the RMSE, the closer the simulations are to the actual values.

The formula for MAE is as follows:

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{n}{\sum }_{i=1}^n{y}_i-k_i$$

(4)

where y_i is the observed value, k_i is the simulated value, and n is the number of samples. The smaller the MAE, the better the simulations are.

The formula for MBE is as follows:

$$\mathrm{M}\mathrm{B}\mathrm{E}=\frac{{\sum }_{i=1}^n(k_i-y_i)}{n}$$

(5)

where y_i is the observed value, k_i is the simulated value, and n is the number of samples. The smaller the MBE, the closer the simulations are to the observations.

The formula for calculating R is as follows:

$$R=\frac{{\sum }_{i=1}^n(y_i-\overline{y})(k_i-\overline{k})}{\sqrt{{\sum }_{i=1}^n{{(y}_i-\overline{y})}^2}\sqrt{{\sum }_{i=1}^n{{(k}_i-\overline{k})}^2}}$$

(6)

where y_i is the observed value, $\overline{y}$ is the average observed value, k_i is the simulated value, $\overline{k}$ is the average of the simulated values, and n is the number of samples.

3. Results

3.1. Impact of Nearest One or Four Grid Boxes

Figure 2 shows the relationship between the simulated and observed monthly averages of δ¹⁸O in precipitation without altitude correction, and two methods using the nearest one (method 1) or four (method 2) grid boxes are applied for simulations. In general, the two methods have similar temporal trends in the study region. Among these sampling sites, the observed δ¹⁸O values in precipitation are usually higher than the simulations, that is, the simulations of isoGSM2 have more depleted isotopes than the observations in the study region.

Several statistical measures are used to examine the performance of methods using the near one or four grid boxes without altitude correction (

Table 2. RMSE, MAE, MBE, and R of simulated monthly average δ¹⁸O using the two methods before altitude correction for each site.

Method	Site	RMSE (‰)	MAE (‰)	MBE (‰)	R
1	Anning	5.88	4.92	−3.74	0.28
	Gaolan	4.24	3.62	−3.02	0.49
	Daheng	2.73	2.19	−1.39	0.82
	Hezui	3.79	2.95	−2.26	0.74
	Doujiashan	4.01	3.24	−3.24	0.65
	Renshoushan	5.44	4.94	−3.81	0.66
	Yongdeng	4.33	3.60	−2.25	0.56
	Wushengyi	4.06	3.05	−2.62	0.57
	Yuzhong	4.90	4.05	−1.27	0.24
	Gongjing	3.35	2.85	−0.26	0.64
	Lanzhou	5.16	4.14	−3.01	0.47
	Xiaguanying	4.75	3.62	−0.76	0.10
2	Anning	4.99	4.04	−3.01	0.45
	Gaolan	3.96	3.42	−2.91	0.45
	Daheng	2.56	2.06	−1.13	0.83
	Hezui	4.06	3.30	−2.86	0.77
	Doujiashan	2.79	2.11	−1.99	0.67
	Renshoushan	4.41	3.94	−2.98	0.81
	Yongdeng	4.52	3.80	−2.34	0.50
	Wushengyi	4.04	3.08	−2.70	0.57
	Yuzhong	4.93	4.13	−1.92	0.30
	Gongjing	3.10	2.84	−0.67	0.71
	Lanzhou	4.23	3.38	−2.00	0.60
	Xiaguanying	4.57	3.32	−1.13	0.19

). According to the arithmetic averages and medians of the statistical measures among these sampling sites, before altitude correction, the performance using the nearest four grid boxes (method 2) to the target site is better than that using the nearest box (method 1). The arithmetic averages of δ¹⁸O RMSE of methods 1 and 2 are 4.39‰ and 4.01‰, respectively, and the average difference in δ¹⁸O RMSE is 0.37‰. The median of the δ¹⁸O RMSE difference for each site is 0.22‰. Similarly, the averages of correlation coefficient are 0.52 and 0.57, respectively, indicating an increase by 0.05 from method 1 to method 2. The median of correlation coefficient difference for each site is also 0.05. The pattern for MAE and MBE also have similar findings.

For the GNIP Lanzhou site with the longest observations (Table 2), there is clear difference between methods 1 and 2. The δ¹⁸O RMSE values of methods 1 and 2 are 5.16‰ and 4.23‰, respectively. The latter is less than the former by 0.93‰, which is larger than the station average previously mentioned (0.37‰). The correlation coefficient of the methods 1 and 2 are 0.47 and 0.60, respectively, and there is an increase of 0.13 from method 1 to method 2.

It should be noticed that in the valley topography of the study area, the population is usually distributed at relatively lower altitudes close to the river, and then the sampling sites with manual supports usually have a lower altitude than the regional mean. This may cause a systemic bias that the low altitude may have larger weightings in observations, and the higher altitudes are not well represented by the existing observations. Specifically, the sites on the mountains or plateaus outside the urban area with low altitudes across the study region are limited. According to the altitude effect of precipitation isotopes, the high altitudes usually have a lower isotope value, and the sampling-caused bias may cause the simulated δ¹⁸O to be lower than the observations to some degree.

3.2. Relationship between Altitude Error and Simulation Performance

Figure 3 shows the relationship between altitude error and precipitation isotope simulation performance using the two methods. The negative correlation between altitude error and seasonal δ¹⁸O MBE can be seen for each season. As the altitude error increases, the isotope MBE decreases. The linear regression slopes of methods 1 and 2 are −0.20‰/100 m and −0.41‰/100 m in spring, −4.40‰/100 m and −4.22‰/100 m in summer, −1.27‰/100 m and −0.44‰/100 m in autumn, and −1.11‰/100 m and −1.49‰/100 m in winter, respectively. The strongest altitude isotopic gradient is in summer, and the weakest is in winter. Most seasons have a negative correlation coefficient ≤ −0.5, except winter with limited precipitation observations. For method 1, among the five sites with relatively long observations (Lanzhou, Anning, Yuzhong, Gaolan, and Yongdeng), the Yongdeng site has the smallest altitude error (25.5 m), while Lanzhou and Anning have the largest altitude errors (993.9 m and 962.9 m), respectively. For method 2, among the five sites with long observations, the Yongdeng site has the smallest elevation error of 62.1 m, while Lanzhou and Anning have the largest elevation errors (571.9 m and 585.8 m), respectively. Generally, the sites with low altitude errors correspond to the sites with better performance of precipitation isotopes according to the models. Between the two methods, the altitude error of method 1 is usually larger than that of method 2.

3.3. Improvement in Simulations Corrected by Altitude

Based on the relationship between seasonal δ¹⁸O MBE and altitude error, altitude correction can be conducted on the isoGSM2 monthly data. Assuming that the precipitation isotope fractionation and altitude gradient is a constant, the simulated results are corrected. Figure 4 shows the simulations after altitude correction as well as the observed values for each sampling site. Compared to Figure 2 and Table 2 before altitude correction, the accuracy of the simulated δ¹⁸O in precipitation shown in Figure 4 and

Table 3. Altitude error, RMSE, MAE, MBE, and R of simulated monthly average δ¹⁸O using the two methods after altitude correction for each site.

Method	Site	Altitude Error (m)	RMSE (‰)	MAE (‰)	MBE (‰)	R
1	Anning	962.8	4.07	3.27	−0.12	0.43
	Gaolan	474.5	3.05	2.23	−0.15	0.46
	Daheng	113.5	2.42	1.99	0.49	0.84
	Hezui	480.5	2.91	2.03	0.26	0.75
	Doujiashan	785.8	1.85	1.41	0.21	0.79
	Renshoushan	853.8	3.55	2.59	−0.56	0.73
	Yongdeng	24.5	3.20	2.41	−0.42	0.69
	Wushengyi	−154.5	2.93	2.13	−1.35	0.80
	Yuzhong	−117.6	4.36	3.49	0.39	0.35
	Gongjing	−725.6	2.10	1.52	0.08	0.89
	Lanzhou	993.8	3.72	2.84	0.70	0.62
	Xiaguanying	−643.6	4.00	3.19	−0.13	0.38
2	Anning	585.8	3.80	2.96	−0.53	0.52
	Gaolan	−237.7	2.95	2.43	−1.32	0.44
	Daheng	−14.7	2.22	1.79	0.39	0.85
	Hezui	661.0	2.45	1.75	−0.32	0.84
	Doujiashan	343.6	1.48	1.12	0.26	0.87
	Renshoushan	489.4	3.10	2.44	−0.67	0.82
	Yongdeng	62.1	3.48	2.68	−0.62	0.63
	Wushengyi	−117.2	2.70	2.11	−1.35	0.82
	Yuzhong	143.3	6.26	5.20	−2.82	0.11
	Gongjing	−568.4	1.91	1.62	0.20	0.90
	Lanzhou	571.9	3.56	2.79	0.50	0.66
	Xiaguanying	−497.4	3.96	3.05	−0.12	0.40

has been improved. In addition, the differences between methods using methods 1 and 2 are also weakened, and the average differences are 0.02‰ for root mean square error and −0.01 for correlation coefficient.

In Table 3, the arithmetic averages of RMSE among these sampling sites are 3.18‰ using method 1 and 3.16‰ using method 2, which are less than those before altitude correction (4.39‰ using method 1 and 4.01‰ using method 2). The arithmetic averages of correlation coefficient are 0.64 using method 1 and 0.66 using method 2, and are also higher than those before altitude correction (0.52 and 0.57). In the GNIP Lanzhou site, the RMSE values are 3.72‰ using method 1 and 3.56‰ using method 2, and are also better than those without correction (5.16‰ and 4.23‰).

The greater the altitude error, the more obvious the correction effect. The terrain of Lanzhou is complex, and the altitude of the simulated data does not match the actual altitude, resulting in differences in results. The two methods have different processes for obtaining altitude, and the error range of method 2 is relatively narrow. Through altitude correction, the model can more accurately simulate the variability in precipitation isotopes, thereby improving the consistency of evaluation indicators.

The Taylor diagram (Figure 5) [38] is used to compare the the two methods before and after correction. In Figure 5, scattered points represent interpolation methods, radial lines represent correlation coefficients, horizontal and vertical axes represent standard deviations, and dotted lines represent root mean square deviation. It can be seen that the Gongjing site is the most sensitive to altitude correction. The elevation difference of the Gongjing site in method 1 is −725.6 m, while the elevation difference in Gongjing for method 2 is −568.4 m, both of which are the most negative among all sites. When the actual altitude is much larger than the simulated value, the obtained results fluctuate more between methods 1 and 2.

4. Discussion

The precipitation isotope simulated using climate models have been widely used in atmospheric studies, but the spatial resolution is usually low. As altitude is one of the traditional factors controlling the spatial pattern of precipitation isotopes, altitude correction is needed to downscale the global and regional simulations. In some downscaling or correction cases of precipitation isotopes, altitude is one of the important geographical parameters [18,21]. Here, we provided a relatively practical method in the Chinese Loess Plateau. Comparing to the machine learning method [18] to downscale the simulated isotope in precipitation, more physical controls and microclimate dynamics are considered in this study, which makes it more practical to be used on a local scale. In some European [39] and Asian [21] cases using multiple mathematical methods, as judged by the increase in correlation coefficient and the decrease in RMSE and MAE after correction, we have similar and even better improvements.

The representativeness of sampling network is a factor influencing the corrections. For example, there is only one fixed altitude gradient in the Asian case [21], which may increase the uncertainty from sampling locations. In our study, the altitude gradient is derived from multiple sampling stations, which may reflect the main geomorphological characteristics in this river valley. However, our compiled sampling network is still not enough to cover all the geographical details, and especially the potential incoherence in the windward and leeward should be examined in the future. In addition, the temporal difference should also be improved when necessary.

Here only the altitude is considered to correct the simulations, and other regional or local factors are generally ignored. Although this assumption shows improvements after correction, other potential factors do have an effect. In Lanzhou under a semi-arid climate, the land-use is impacted by urbanization and afforestation [40,41,42]. With the increasing greening level in the study region, the transpiration effect of vegetation cannot be ignored, and coal combustion generates a large amount of water vapor, which enhances the local water vapor recycling rate. Further research and improvement are needed to understand the impact of topography and related factors on precipitation isotopes.

5. Conclusions

Using the isoGSM2 simulation data and observed isotope data from 12 sites across a typical river valley of the Chinese Loess Plateau, we presented a practical method to improve the climate model simulations. We showed the influences of altitude on precipitation isotope errors. According to the linear relationship between altitude error and isotope simulations, we corrected the simulated isotope composition. After altitude correction in this study, the root mean square error across the sampling sites decreases by 1.21‰ or 0.86‰ using the nearest one or four grid boxes, respectively, and the correlation coefficient increases by 0.13 or 0.08, respectively. The differences between methods using the nearest one or four grids are also weakened. Topography correction, especially the altitude correction of precipitation isotopes, should be considered to downscale the simulations of climate models.