Elevation Correction of ERA5 Reanalysis Temperature over the Qilian Mountains of China

Abstract

Air temperature acts as a key indicator of climate change. In regions with high elevations and scarce meteorological stations, reanalysis temperature datasets are vital for estimating temperatures. However, due to the presence of biases in the observational data of these reanalysis datasets, it becomes necessary to perform bias correction to augment the accuracy of modeling and prediction. In the present study, a temperature lapse rate model was utilized to correct the ERA5 reanalysis temperature data within the Qilian Mountains (QLMs) in China from 1979 to 2017. The research results show that the constructed temperature lapse rate can effectively reflect the vertical temperature change characteristics in the Qilian Mountains. As the altitude increases, the absolute value of the temperature lapse rate on the northern slope decreases, while the absolute value of the temperature lapse rate on the southern slope increases. The accuracy of the corrected ERA5 temperature data is significantly improved, especially in winter. Among the 17 meteorological stations, 13 stations show a statistically significant improvement in accuracy after correction in winter, accounting for approximately 76.5% of the total stations. This study can provide a reliable data reference for climate research, ecological environment monitoring, and other fields in the Qilian Mountains area.

1. Introduction

The Qilian Mountains (QLMs) serve as a crucial ecological barrier and a significant water conservation area in the northwest of China [1,2]. The study of climate change in the Qilian Mountains has drawn considerable attention from scientists. Temperature is the most direct and important indicator for researching climate change in the Qilian Mountains [3,4]. The rising temperature in the Qilian Mountains has led to a series of ecological problems, such as glacier retreat and permafrost thawing, which have a significant impact on the water resources and water cycle around the Qilian Mountains [2,5]. Therefore, the study of temperature changes in the Qilian Mountains has always been of great concern.

Although previous researchers have used observed temperature data from stations to detect the temperature changes in the Qilian Mountains [6], the complex terrain and climate factors within the mountains have resulted in a scarcity and uneven distribution of meteorological stations in higher altitude areas. Therefore, observed temperature data are insufficient to confirm more detailed temperature change characteristics in the Qilian Mountains [3,6]. Although satellite and remote sensing products make up for the shortcomings of observation stations, their time series is short, and they are easily affected by factors such as cloud cover, which limits the reliability of satellite remote sensing data in detecting temperature change [7,8]. Although there are many types of climate models that can predict future temperature trends, climate models have the disadvantage of often simplifying complex physical processes in the climate system, which may result in inaccurate simulations of regional climate and extreme weather events [9,10]. Therefore, a high-resolution, long time-series, and high-precision reanalysis temperature dataset is a fundamental prerequisite for accurately analyzing temperature changes in the Qilian Mountains [3,11,12,13,14].

Although reanalysis temperature data have small errors at the global scale and can be considered real observational data, their applicability still needs to be rigorously tested when applied to small-scale research. Previous evaluation results have found that when reanalyzing reanalysis temperature data for studying temperature changes in the Qilian Mountains, caution still needs to be exercised [11,12,13,14]. Therefore, it is necessary to correct the reanalysis temperature data to improve its accuracy. Wu et al. [15] employed the random forest model to carry out the reconstruction of ERA5 air temperature (2 m) at Dome A in Antarctica. The results indicated that the temperature error of ERA5 was notably reduced after being calibrated by the random forest. Hanoi et al. [16] utilized regression calibration to rectify the evapotranspiration (ET0) data in the United States. Their findings demonstrated that the regression calibration procedure significantly enhanced the ET0 forecast performance, particularly in regions with coastal locations or complex terrains. Jaroslav et al. [17] applied a neural network-based calibration model to correct ECMWF data. The results revealed that the parameterized model surpassed the standard ECMWF prediction in terms of accuracy and was closer to the forecast accuracy of the local numerical weather prediction model. Regarding the correction of reanalysis temperature data, the temperature lapse rate model is the most commonly used correction method [18,19,20,21]. The temperature lapse rate method can effectively capture vertical temperature changes, being highly applicable across various terrains and climates, and in the study of using the temperature lapse rate model to correct reanalysis temperature data, the most commonly used temperature lapse rates are calculated based on observed values [14]. However, in complex terrain areas, especially in high mountain areas, there are few observation stations, making it difficult to construct reliable temperature lapse rates [14]. Therefore, using reanalysis geopotential heights and temperature data from different pressure layers to construct a temperature correction model that does not rely on ground stations plays a crucial role in improving the accuracy of reanalysis temperature data [18,19,20,21].

The main objective of this study is to utilize ERA5 data to construct a temperature lapse rate model that does not rely on ground observation stations. By applying this model to correct ERA5 reanalysis temperature data in the Qilian Mountains region, we aim to enhance the accuracy and reliability of the data, thereby facilitating in-depth research on climate change, ecological environment evolution, and water resource management in the Qilian Mountains.

2. Data and Methods

2.1. Study Area

The Qilian Mountains are located on the northeastern border of Qinghai Province and the western border of Gansu Province in China, spanning from 97°25′ to 103°46′ east longitude and from 36°43′ to 39°36′ north latitude. They are one of the major mountain ranges in China. The annual average temperature of the Qilian Mountains is 1–4 °C, and the annual average precipitation is 400 mm. The precipitation throughout the year is mainly concentrated from May to September. The annual average minimum temperature, around −11 °C, occurs in January, while the average maximum temperature, around 15 °C, occurs in July [4,5,6].

2.2. ERA5 Reanalysis Data

ERA5 reanalysis data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) [22,23,24]. The ERA5 data selected in this study include monthly temperature (2 m) data, geopotential grid points, geopotential height, and geopotential temperatures at different pressure layers. The resolution of ERA5 reanalysis monthly temperature (2 m) data is 0.25° × 0.25°, with a spatial range of 35.75–40° N and 93.5–104° E. The time series of ERA5 reanalysis data used in this study is 1979–2017. Figure 1 shows the spatial distribution of the ERA5 grid points in the Qilian Mountains and its surrounding areas.

Table 1. Information of 17 meteorological stations in the Qilian Mountains.

Station Number	Station Name	Latitude (°)	Longitude (°)	HOBS (m)	HERA5 (m)	Δh (m)
1	Jiu Quan	39.67	98.72	1470	1372.69	97.31
2	Gao Tai	39.38	99.72	1357	1750.63	−393.63
3	Zhang Ye	38.92	100.58	1550	1569.94	−19.94
4	Shan Dan	38.78	101.08	1760	1948.03	−188.03
5	Yong Chang	38.23	101.97	1987	2200.30	−213.30
6	Wu Wei	38.08	102.92	1525	1534.51	−9.51
7	Wu Shaoling	37.20	102.87	3045	3525.72	−480.72
8	Gao Lan	36.55	103.67	2032	1920.80	111.20
9	Leng Hu	38.75	93.58	2762	2906.15	−144.15
10	Tuo Te	38.87	98.37	3460	4063.61	−603.61
11	Ye Niugou	38.62	99.35	3200	3931.52	−731.52
12	Qi Lian	38.18	100.30	2800	3579.73	−779.73
13	Da Chaidan	37.83	95.28	3000	3464.35	−464.35
14	De Lingha	37.25	97.13	2762	3005.05	−243.05
15	Gang Cha	37.33	100.17	3100	3302.15	−202.15
16	Men Yuan	37.45	101.62	2800	3524.30	−724.30
17	Min He	36.23	102.93	1900	2076.61	−176.61

Δh is equal to the H_OBS minus the H_ERA5.

shows the basic information of 17 meteorological stations. The geopotential height of the pattern grid points is a constant value, which is the altitude of the ERA5 grid points (H_ERA5). Dividing the downloaded geopotential height by the gravitational acceleration converts the altitude of each grid point. In order to correct the ERA5 reanalysis temperature (2 m) data, this study also downloaded the geopotential height and temperature data of five pressure layers at 500 hPa, 600 hPa, 700 hPa, 850 hPa, and 925 hPa. Each pressure layer contains ERA5 geopotential height and temperature information. The resolution, spatial range, and time series of ERA5 data at pressure levels are consistent with ERA5 reanalysis monthly average temperature (2 m) data. The geopotential height divided by the gravitational acceleration was converted into the altitude of each grid point in the pressure layer. ERA5 reanalysis geopotential height and temperature are mainly used to calculate the temperature lapse rate. Attention should be paid to the fact that the key reason for opting for these pressure layers lies in that their geopotential heights are capable of reflecting the actual characteristics of the mountain climate and covering the altitude range of most stations in the QLMs, which is conducive to subsequent correction and comparison. The altitudes corresponding to the five pressure layers are around 5000 m, 4000 m, 3000 m, 1500 m, and 500 m, respectively [18].

2.3. Observed Data

The observed temperature data include data from 17 meteorological stations inside and outside the Qilian Mountains from 1950 to 2022, downloaded from the National Meteorological Science Data Center (http://data.cma.cn/, accessed on 9 March 2025). The spatial distribution and specific information of 17 meteorological stations are shown in Figure 1 and Table 1. The data from 1979 to 2017 are complete and without missing information, which is suitable for the evaluation and downscaling result verification of ERA5 reanalysis data [18]. These 17 meteorological stations are located between an altitude of 1000 m and 3500 m. Figure 1 and Table 1 list the station names, latitude, longitude, station altitude, ERA5 grid point altitude, and the altitude difference (Δh) between the ERA5 grid points and meteorological stations for 17 meteorological stations (station altitude minus ERA5 reanalysis grid point altitude). The months corresponding to seasons are divided into spring (March to May), summer (June to August), autumn (September to November), and winter (December to February).

2.4. Correction Method

2.4.1. Construction of Temperature Lapse Rate

The temperature lapse rate is the rate at which temperature decreases with increasing altitude, generally around −6.0 °C/km, which means that for every 1000 m increase in elevation, it decreases by 6 °C. This study uses the geopotential height and temperature data of different pressure layers to calculate the ERA5 reanalysis temperature lapse rate. Based on the reanalysis of geopotential height and temperature, four types of temperature lapse rates were constructed (

Table 2. The temperature lapse rate (Γ) and reference temperature value (T_ref) of the four correction methods used in this study.

Γ	Tref	Station Elevation Ranges
Γ500_600	TERA_2m	4000–5000 m
Γ600_700	TERA_2m	3000–4000 m
Γ700_850	TERA_2m	1500–3000 m
Γ850_925	TERA_2m	500–1500 m

). These four corresponding temperature lapse rates are Formulas (1) to (4): Rate I (Γ_{500_600}), Rate II (Γ_{600_700}), Rate III (Γ_{700_850}), and Rate IV (Γ_{850_925}). Rates I to IV can be calculated using Formulas (1) to (4) to obtain the vertical temperature lapse rates at five pressure levels, represented by Γ_{500_600}, Γ_{600_700}, Γ_{700_850}, and Γ_{850_925}. Among them, T₅₀₀, T₆₀₀, T₇₀₀, T₈₅₀, and T₉₂₅ represent the temperature at pressure levels of 500 hPa, 600 hPa, 700 hPa, 850 hPa, and 925 hPa, respectively. H₅₀₀, H₆₀₀, H₇₀₀, H₈₅₀, and H₉₂₅ represent heights at pressure levels of 500 hPa, 600 hPa, 700 hPa, 850 hPa, and 925 hPa, respectively. This study compared and analyzed the changing characteristics of these four temperature lapse rates on different time and spatial scales.

2.4.2. ERA5 Reanalysis Correction of Temperature Data

An elevation correction model was constructed that does not rely on ground observation stations based on the temperature lapse rate calculated from the ERA5 geopotential height and temperature [18,19,20,21]. Formula (5) was used to correct the ERA5 reanalysis temperature data, where T_t is the corrected reanalysis temperature data at the ERA5 grid point that is nearest to each meteorological station. T_ref is the ERA5 reanalysis monthly averaged temperature (2 m) data, which are planned to be corrected; Δh = H_OBS − H_ERA5, where H_OBS is the altitude of each meteorological station; and H_ERA5 is the ERA5 mode grid point height divided by the gravitational acceleration. Δh was calculated, as shown in Table 1. All parameters in Formula (5) were derived from reanalysis data and completely independent of ground observation stations. The calculation of the vertical temperature lapse rate was based on ERA5 reanalysis potential data. In this study, the value of Γ was determined based on the altitude of the meteorological station. For example, if the altitude of the meteorological station is 500 m, the value of Γ is calculated based on the geopotential heights of 850 hPa and 925 hPa, which represent altitudes of 1500 m and 500 m, respectively (Figure 2). If the altitude of the meteorological station is 3500 m, the values of Γ are calculated based on the geopotential heights and temperatures at 600 hPa and 700 hPa, which represent elevations of 4000 m and 3000 m, respectively (Figure 2). In summary, the altitude of meteorological stations represented by Γ_{500_600}, Γ_{600_700}, Γ_{700_850}, and Γ_{850_925} are ≥4000 m, 3000–4000 m, 1500–3000 m, and ≤1500 m, respectively.

2.4.3. Verification of ERA5 Reanalysis Temperature Correction Results

Based on the original ERA5 reanalysis temperature (2 m) data, station observation data, and corrected ERA5 data, error indicators, such as bias and root mean square error (RMSE), were used to evaluate the correction results. For example, the RMSE values before and after correction were compared. If the RMSE value decreases, it indicates that the data quality improves after correction. When comparing the error between the corrected ERA5 reanalysis data and meteorological station data, we did not employ interpolation methods. Instead, we directly identified the nearest ERA5 grid points to each meteorological station. This can avoid the error caused by the interpolation method.

Γ_{500_600} = (T₅₀₀ − T₆₀₀)/(H₅₀₀ − H₆₀₀)

(1)

Γ_{600_700} = (T₆₀₀ − T₇₀₀)/(H₆₀₀ − H₇₀₀)

(2)

Γ_{700_850} = (T₇₀₀ − T₈₅₀)/(H₇₀₀ − H₈₅₀)

(3)

Γ_{850_925} = (T₈₅₀ − T₉₂₅)/(H₈₅₀ − H₉₂₅)

(4)

T_t = T_ref + Γ × Δh

(5)

3. Results

3.1. Time Variation Characteristics of Temperature Lapse Rates

Figure 3 shows the variation characteristics of four temperature lapse rates over 12 months. The temperature lapse rates were averaged over the entire Qilian Mountains and the whole study period of 1979–2017. Overall, these four temperature lapse rates are around −6 °C/km, which conforms to the general law of temperature lapse rates. From

Table 3. Values of monthly temperature lapse rates averaged over the entire Qilian Mountains and the whole study period of 1979–2017 (°C/km).

Month	Γ500_600	Γ600_700	Γ700_850	Γ850_925
January	−6.76	−5.70	−5.76	−6.51
February	−6.90	−6.05	−6.20	−6.53
March	−7.12	−6.59	−6.57	−6.51
April	−7.29	−7.08	−6.57	−6.28
May	−7.16	−7.16	−6.15	−5.74
June	−6.86	−7.03	−5.52	−5.05
July	−6.55	−6.68	−4.95	−4.50
August	−6.56	−6.52	−4.99	−4.61
September	−6.69	−6.63	−5.75	−5.51
October	−6.98	−6.65	−6.34	−6.32
November	−7.09	−6.28	−6.09	−6.53
December	−6.80	−5.74	−5.68	−6.50

, it can be seen that the maximum value of Γ_{500_600} occurs in April (−7.29 °C/km), the maximum value of Γ_{600_700} occurs in May (−7.16 °C/km), the maximum value of Γ_{700_850} occurs in March and April (−6.57 °C/km), and the maximum value of Γ_{850_925} occurs in February and November (−6.53 °C/km).

3.2. Spatial Variation Characteristics of Temperature Lapse Rates

Figure 4 shows the spatial distribution characteristics of temperature lapse rates at different pressure layers of the Qilian Mountains. For Γ_{500_600} and Γ_{600_700}, the absolute value of the temperature lapse rate is highest on the southern slope of the Qilian Mountains, with Γ_{500_600} having the lowest absolute value on the northern slope of the Qilian Mountains (Figure 4a) and Γ_{600_700} having the lowest absolute value within the Qilian Mountains (Figure 4b). For Γ_{700_850} and Γ_{850_925}, the absolute value of the temperature lapse rate is highest on the northern slope of the Qilian Mountains, followed by the interior of the Qilian Mountains, and the absolute value of the temperature lapse rate is lowest on the southern slope of the Qilian Mountains (Figure 4c,d). The above results indicate that as the altitude increases, the absolute value of the temperature lapse rate on the northern slope decreases, while the absolute value of the temperature lapse rate on the southern slope increases, which may be caused by the differences in moisture between the southern slope and the northern slope in the QLMs.

3.3. Correction Results of Annual Mean Temperature Data

Figure 5 shows a comparison of temperature bias and root mean square error before and after correction for 17 stations in the Qilian Mountains. Uncorrected bias refers to the deviation between the observed data and the ERA5 reanalysis temperature data of the nearest grid point, while corrected bias is the deviation between the observed data and the corrected ERA5 reanalysis temperature data of the nearest grid point. Uncorrected RMSE is the root mean square error between the observed data and the ERA5 reanalysis temperature data of the nearest grid point, and corrected RMSE is the root mean square error between the observed data and the corrected ERA5 reanalysis temperature data of the nearest grid point. When seeking the nearest grid point to the station, both the horizontal and vertical distances between the measured station and the ERA5 grid point were taken into account. For the temperature bias changes before and after correction, the absolute value of temperature bias decreased at most stations after correction, indicating that the correction was effective, but there were a few stations (such as No. 2 and No. 7) where the absolute value of bias increased after correction. For the root mean square error before and after correction, the root mean square error of 10 meteorological stations after correction decreased compared to before correction, indicating that the temperature lapse rate model is effective for correcting the ERA5 reanalysis temperature data closest to these 10 meteorological stations, such as No. 8, where the uncorrected bias is 1.11 °C and the corrected bias is 0.40 °C, indicating that correct method is effective in correcting the temperature (

Table 4. Correction results of ERA5 annual average temperature data for 17 stations in the Qilian Mountains.

No.	Uncorrected Bias	Corrected Bias	Uncorrected RMSE	Corrected RMSE
1	0.15	−0.48	0.61	0.77
2	0.84	3.44	1.21	3.54
3	−0.04	0.09	1.06	1.05
4	−1.42	−0.18	1.60	0.76
5	−0.64	0.77	1.03	1.14
6	0.35	0.41	0.87	0.90
7	−1.42	1.60	2.12	2.28
8	1.11	0.40	1.42	1.03
9	−0.05	0.74	0.66	1.09
10	−6.03	−2.51	6.32	3.14
11	−5.21	−0.99	5.48	1.93
12	−6.71	−2.06	6.92	2.57
13	−1.70	1.61	1.86	1.78
14	−0.69	0.59	0.95	0.89
15	−0.10	1.17	1.07	1.63
16	−6.01	−1.72	6.26	2.30
17	−0.77	0.39	1.12	0.94

). For the other seven meteorological stations, the temperature lapse rate model may not be applicable for correcting the ERA5 reanalysis temperature data closest to them. For stations located in complex terrain areas, such as valleys and steep slopes, the local climate is complex, and the terrain shielding effect may lead to poor correction results. High-altitude stations are more affected by changes in atmospheric circulation and radiation balance, which also affects the correction accuracy.

From Figure 6, it can be seen that the root mean square error of nine meteorological stations after correction in spring is smaller than before correction. For example, at No. 8, the uncorrected bias is 0.99 °C, and the corrected bias is 0.21 °C, showing that the correction method is effective. However, the uncorrected bias at No. 2 is 0.81 °C and the corrected bias is 3.41 °C, showing that the correction method is not effective in correcting the temperature in spring at No. 2 (

Table 5. Bias correction results of ERA5 seasonal temperature data for 17 stations in the Qilian Mountains.

No.	Corrected Bias in Spring	Corrected Bias in Summer	Corrected Bias in Autumn	Corrected Bias in Winter	Uncorrected Bias in Spring	Uncorrected Bias in Summer	Uncorrected Bias in Autumn	Uncorrected Bias in Winter
1	−0.73	−0.74	−0.39	−0.05	−0.09	−0.08	0.24	0.55
2	3.41	3.78	3.52	3.03	0.81	1.17	0.92	0.46
3	−0.34	−0.91	0.31	1.28	−0.49	−1.05	0.19	1.18
4	0.31	−0.34	−0.33	−0.35	−1.04	−1.68	−1.57	−1.4
5	1.08	1.23	0.53	0.23	−0.43	−0.17	−0.89	−1.05
6	0.65	0.89	0.17	−0.07	0.57	0.82	0.11	−0.11
7	2.48	2.56	1.71	−0.34	−0.74	−0.33	−1.38	−3.25
8	0.21	−0.16	0.03	1.53	0.99	0.61	0.72	2.12
9	1.00	−0.37	0.99	1.32	0.15	−0.87	0.14	0.38
10	−3.20	−2.98	−3.00	−0.84	−6.94	−6.27	−6.46	−4.43
11	−1.81	−0.55	−1.93	0.34	−6.23	−4.46	−6.12	−4.02
12	−3.17	−1.88	−2.14	−1.05	−8.08	−5.58	−7.03	−6.13
13	1.74	0.87	1.98	1.87	−1.76	−2.37	−1.39	−1.27
14	0.81	0.25	0.89	0.43	−0.57	−0.53	−0.46	−1.19
15	0.76	1.62	2.09	0.21	−0.54	0.28	0.72	−0.87
16	−3.01	−1.18	−1.85	−0.86	−7.56	−4.57	−6.33	−5.56
17	0.44	0.97	0.22	−0.06	−0.82	−0.27	−0.93	−1.05

). The root mean square error of 10 meteorological stations after correction in summer is smaller than before correction; however, the uncorrected bias at No. 15 is 0.28 °C, and the corrected bias is 1.62 °C, showing that the correction method is not effective in correcting the temperature in summer at No. 15 (Table 5). The root mean square error of eight meteorological stations after correction in autumn is smaller than before correction. The correction results show that at No. 8, the correction method is effective in correcting the temperature in autumn. The correction results show that at No. 2, the correction method is not effective at correcting the temperature in autumn (Table 5). The root mean square error of 13 meteorological stations after correction in winter is smaller than before correction, indicating that the correction effect in winter is the best (

Table 6. Root mean square error correction results of original ERA5 annual seasonal temperature data from 17 Stations in the Qilian Mountains.

No.	Corrected RMSE in Spring	Corrected RMSE in Summer	Corrected RMSE in Autumn	Corrected RMSE in Winter	Uncorrected RMSE in Spring	Uncorrected RMSE in Summer	Uncorrected RMSE in Autumn	Uncorrected RMSE in Winter
1	0.82	0.84	0.55	0.46	0.39	0.42	0.46	0.71
2	3.42	3.82	3.55	3.11	0.87	1.27	1.04	0.85
3	0.45	0.94	0.49	1.43	0.57	1.09	0.42	1.35
4	0.39	0.44	0.50	0.70	1.07	1.7	1.61	1.52
5	1.15	1.27	0.74	0.68	0.58	0.37	1.02	1.23
6	0.76	1.01	0.69	0.67	0.71	0.95	0.68	0.68
7	2.52	2.57	1.87	0.82	0.85	0.38	1.57	3.33
8	0.36	0.32	0.45	1.60	1.03	0.67	0.85	2.16
9	1.05	0.44	1.03	1.36	0.35	0.9	0.32	0.5
10	3.41	2.99	3.44	1.35	7.04	6.28	6.67	4.56
11	2.08	0.59	2.35	0.90	6.31	4.46	6.26	4.1
12	3.26	1.89	2.41	1.36	8.12	5.58	7.11	6.2
13	1.77	0.91	2.01	1.95	1.8	2.39	1.44	1.39
14	0.86	0.45	0.95	0.75	0.65	0.65	0.56	1.34
15	0.84	1.64	2.15	0.90	0.65	0.37	0.88	1.23
16	3.05	1.21	2.04	1.39	7.58	4.58	6.39	5.67
17	0.56	1.02	0.53	0.65	0.89	0.43	1.05	1.24

). In winter, the atmosphere is relatively stable, with weak vertical mixing, and the temperature vertical variation is relatively simple, which is conducive to the application of the correction model. In summer, strong solar radiation leads to uneven ground heating, strong atmospheric convection, and a complex temperature vertical structure, increasing the difficulty of correction.

From Figure 7 and Figure 8, it can be seen that the corrected average temperature and observed temperature are relatively close, and the corrected temperatures reflect the variation in the annual average temperature changes in the Qilian Mountains well. The average observations at 17 meteorological stations from 1979 to 2017 are 4.13 °C, the average ERA5 reanalysis temperature at the ERA5 grid points closest to meteorological stations is 2.47 °C, and the corrected average ERA5 reanalysis temperature at the ERA5 grid points closest to meteorological stations is 4.33 °C, indicating that the corrected temperatures are closer to the observations at 17 meteorological stations from 1979 to 2017 (Figure 7). The temperature trend of annual mean observations, original ERA5, and corrected ERA5 are 0.488 °C/10a, 0.509 °C/10a, and 0.509 °C/10a, respectively, with a rapid increase in 1997. The uncorrected average bias at 17 meteorological stations in 1979–2017 in spring, summer, autumn, and winter is −1.93 °C, −1.49 °C, −1.73 °C, and −1.51 °C, respectively. The corrected average bias at 17 meteorological stations in 1979–2017 in spring, summer, autumn, and winter is 0.04 °C, 0.18 °C, 0.16 °C and 0.39 °C, respectively, indicating that the corrected temperatures are closer to the average observations at 17 meteorological stations in 1979–2017 (Figure 8).

4. Discussion

For Γ_{500_600} and Γ_{600_700}, the temperature lapse rate in winter (December to February) is generally small due to the relatively stable atmosphere in winter, weak vertical mixing, and relatively slow heat exchange. The temperature lapse rate in summer (June to August) is relatively large, mainly due to strong solar radiation, significant ground warming, and strong atmospheric convection, which intensify the vertical variation in temperature. Zhao et al. [18] found that the temperature lapse rates of Γ_{600_700} based on ERA-Interim are larger in summer than in winter, which is similar to this study. Overall, the correction method improved the reliability of ERA5 at most stations, but it is not effective for some stations. For annual and seasonal mean temperature correction, the corrected bias and RMSE are clearly larger than the uncorrected bias at No. 2, which may be caused by the systematic biases in the original data, and the temperature lapse rate model may not be suitable for bias correction of No. 2. For No. 5, the corrected RMSE in spring and summer are larger than that in the uncorrected RMSE; however, the corrected RMSE in autumn and winter is smaller than that in the uncorrected RMSE, which may be caused by complex climatic and terrain factors in No. 5. For No. 16, the corrected RMSE in four seasons is smaller than that in the uncorrected RMSE, showing that the correction method is effective at No. 16. Although this study has achieved certain results, there are still some shortcomings. In complex terrains, such as glacier-covered areas and high mountain valleys, the model may not accurately capture the temperature vertical variation characteristics. Zhao et al. [18] and Gao et al. [20] found that complex terrains are the main factors leading to errors in reanalysis data. In addition, vegetation cover is a factor that affects temperature correction [18,25]. The model’s applicability in different climate conditions and regions also needs to be further improved.

Wu et al. [15] found that the machine learning method can not only enhance the local accuracy of ERA5 reanalysis data at Dome A, but it can also effectively address the issues of outlier correction in long time-series reanalysis data and the insufficient capture of extreme temperatures, which is better than the temperature lapse rate method used in this paper. Jaroslav et al. [17] found that the deep learning method can integrate diverse data, capture non-linearities, and learn complex patterns from real-world data. The deep learning method also has better adaptability to complex terrains and climates and can be updated with new data, while the temperature lapse rate method has significant limitations in these aspects. Future research can further optimize the construction of the temperature lapse rate, combining more observational data and advanced data analysis techniques (such as machine learning algorithms) to improve the accuracy and applicability of the temperature lapse rate. Meanwhile, the corrected ERA5 data can be applied to a wider range of research fields, such as the elevation-dependent warming (EDW) characteristics in the Qilian Mountains, providing a more comprehensive scientific basis for the sustainable development of the Qilian Mountains region [4,26]. This study only corrected ERA5 reanalysis temperature data. In future research, other ERA5 data can be corrected, such as ERA5 reanalysis precipitation data, humidity data, wind speed data, etc. [3]. In future studies, downscaling research can also be conducted on ERA5 reanalysis data to obtain high-resolution temperature datasets of the Qilian Mountains [21,27]. It should be noted that this study did not differentiate the impacts of dry and moist adiabatic processes that might influence the temperature lapse rate in the Qilian Mountains, and these deserve further research. Other datasets (such as satellite or model data) can be studied in future research. The accurate temperature data can be used to evaluate the impact of climate change on the ecological system of the Qilian Mountains, providing a basis for formulating ecological protection and restoration policies.

5. Conclusions

The research results show that the constructed temperature lapse rate model effectively improves the accuracy of the ERA5 reanalysis temperature data in the Qilian Mountains. With increasing altitude, the absolute value of the temperature lapse rate on the northern slope decreases, while the absolute value of the temperature lapse rate on the southern slope increases. The correction method reduces the biases between the reanalysis data and the observed data, especially in winter, which may be due to the relative atmosphere in winter. The corrected temperature data are reliable data support for climate research, ecological environment monitoring, and water resource management in the region. For example, in the study of glacier changes, more accurate temperature data can help to better understand the melting rate of glaciers and predict their future trends. In the prediction of extreme weather events, the corrected temperature data can be used as an input parameter for meteorological models to improve prediction accuracy and enable early warning and response measures. This provides more reliable temperature data references for climate research, ecological environment monitoring, water resource management, and other fields in the Qilian Mountains regions.