Introduction

Precipitation is a key factor when studying hydrological and meteorological and plays an important role in water cycling and energy exchange processes (Xie and Arkin 1997; Liu et al. 2008). In addition, precipitation is related to the conditions of the underlying surface (Defriesr 1994; Ding et al. 2007; Jia et al. 2011), including the Digital Elevation Model (DEM) topography, slope, aspect, and Normalized Difference Vegetation Index (NDVI), et al. Thus, obtaining high-resolution precipitation data can substantially affect the temporal and spatial precision of precipitation distributions (Bindlish and Barros 2000; Feidas 2010; Hirpa et al. 2010). To get more high-resolution (spatial and temporal) precipitation data for the Mountains region, different downscaling techniques (dynamical and empirical statistical) were used to “downscale” precipitation data with reanalysis data, climate models data, and remote sensing data from global to regional and local scales (Lloyd 2005; Benestad 2010; Wagner et al. 2012).

Traditional studies on the temporal and spatial characteristics of precipitation are reliant on actual station data, although obvious differences value will occur if only ground observation data are used due to the large elevational fluctuations in mountain areas and the sparse distribution of meteorological stations (Wilheit 1986). Recently, remote sensing satellite data have been used in precipitation studies to improve the precision and accuracy of the results, and remote sensing data include the Global Precipitation Climatology Project (GPCP, Huffman et al. 1997, 2001, 2009), Global Satellite Mapping of Precipitation (GSMaP, Kubota et al. 2000), and Tropical Rainfall Measuring Mission (TRMM, Kummerow and Barnes 1997, Kummerow et al. 2000; Huffman et al. 2007; Almazroui 2011; Liu et al. 2015a). However, remote sensing satellite data with low spatial resolution cannot precisely reflect the temporal and spatial distribution of regional precipitation. Therefore, spatial downscaling is required for remote sensing satellite precipitation products to achieve a higher precision.

Previous studies on downscaling remote sensing satellite precipitation products have considered the effects of topography and vegetation (Turk and Miller 2005; Jia et al. 2011). For example, Guan et al. (2009) performed a downscaling analysis on Next Generation Radar (NEXRAD) data based on the topographical factors. Immerzeel et al. (2009) established a non-linear regression model between TRMM 3B43 precipitation data and a Moderate Resolution Imaging Spectroradiometer (MODIS) vegetation index based on the correlation between the vegetation index and precipitation to increase the TRMM resolution by up to 1 km. Jia et al. (2011) performed a downscaling analysis on TRMM 3B43 data according to NDVI and DEM data. Xu et al. (2015) used a new algorithm by introducing a regional regression model termed as geographically weighted regression (GWR) to downscale the TRMM 3B43 data. Although previous downscaling analyses of remote sensing satellite data have involved vegetation index and topography, the study areas were mainly concentrated in plains or basins instead of areas at high elevation and with complex underlying surfaces (Immerzeel et al. 2009; Jia et al. 2011). Therefore, these downscaling processes need to be verified in mountain areas. Tianshan Mountains is the birthplace of many inland rivers in the arid area of Northwest China (Yuan et al. 2003; Li et al. 2006). The precipitation in Chinese Tianshan Mountains not only determines the total amount of regional water resources but also directly affects the distribution of water resources, the formation of river runoff, the distribution and development of Alpine glacier and snow, then directly related to the ecological environment and socio-economic development in the middle and lower reaches (Wang et al. 2015). Due to the limitation of the observation stations, it is difficult to obtain high-resolution (spatial and temporal) precipitation data in Chinese Tianshan Mountains. Therefore, how to utilize the limited observational data of stations, integrate the ground observations, spatial interpolation, and satellite remote sensing to quickly assimilate and fuse these data of precipitation is the hotspot issues (Bindlish and Barros 2000; Feidas 2010).

The aims of this study are to (1) analyze precision of TRMM 3B43 during 2014–2016 in the middle part of Chinese Tianshan Mountains; (2) employ the DEM with 3″ (approximately 90 m) in spatial resolution, NDVI with 1 km in spatial resolution and the TRMM precipitation data with 0.25° in spatial resolution to downscale the TRMM 3b43 to 1-km spatial resolution. The precision of the results of downscaling was verified by comparison with the measurements of stations.

Material and methods

Study area

The Chinese Tianshan Mountains is one of the largest mountain ranges located in Central Asia and transverse part of China, Kazakhstan, Kyrgyzstan, and Uzbekistan. Approximately 2/3 of the Tianshan Mountains is in the Xinjiang Uygur autonomous, China. The Chinese Tianshan Mountains are the dividing line between north and south Xinjiang and located between latitudes 39.6° N and 45.5° N and longitudes 73.5° E and 96.1° E (Wang et al. 2011). The principal of Chinese Tianshan Mountain runs east to west at elevations ranging from − 188 to 8806 m (Fig. 1).

Fig. 1
figure 1

The location of the Chinese Tianshan Mountains and the location of the 16 metrological stations

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The precipitation of Chinese Tianshan Mountains is dominated by the westerly circulation (Liu et al. 2015b). Therefore, the Tianshan Mountains has relatively abundant precipitation comparing with the average precipitation of arid central Asia (Schiemann et al. 2008). The annual precipitation of Chinese Tianshan Mountains shows spatial variation with large precipitation in the northwestern region and small precipitation in the southeastern (Yuan et al. 2001; Zhong et al. 2017). Based on the integrity and continuity of the precipitation data, this paper performed a downscaling analysis of TRMM precipitation data in the middle part of the Chinese Tianshan Mountains (41° 30′ ~ 44° 36′ N, 80° 64′ ~ 87° 24′ E).

Meteorological station data

Precipitation data from meteorological observation stations are provided by the China meteorological data sharing service (http://www.cma.gov.cn/2011qxfw/2011qsjgx/). There are 16 metrological stations throughout the Chinese Tianshan area (Wenquan, Yining, Zhaosu, Urumqi, Baluntai, Dabancheng, Kumishi, Bayanbulak, Bycheng, Korla, Torugart, Wuqia, Kashgar, Akqi, Barkol, and Yiwu). To verify the model results, ground measurements of middle part of study region were selected from the Yining, Kumishi, Bayanbulak, and Baluntai.

Tropical Rainfall Measuring Mission

The TRMM satellite was developed by the National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration Agency (JAXA) and launched in November 1997. The track of satellite was set at an altitude of around 400 km, an inclination of 35° and the cycle of 92.5 min (Fleming et al. 2011). The aim of the TRMM is to provide the data for more scientific understanding of global energy and water cycling based on precipitation and latent heat (Kummerow and Barnes 1997; Kummerow et al. 2000). Since the year 1997, the products have updated several algorithms and techniques (Haddad et al. 1997; Iguchi et al. 2000; Yang et al. 2015, 2017, 2018).

SRTM DEM

The Shuttle Radar Topography Mission (SRTM) was established by National Aeronautics and Space Administration (NASA) and National Intelligence Mapping Agency (NIMA) and launched in February 2000. It provided free surface elevation information for meeting all kind needs of public. The dataset coverage extends from 56° S to 60° N by latitude (Reuter et al. 2007).

Normalized Difference Vegetation Index (NDVI)

Aim at detecting and monitoring the variety of vegetation and extraction of canopy biophysical parameters, Normalized Difference Vegetation Index (NDVI, Running et al. 1994; Justice et al. 1998; Huete et al. 2002) contains consistent, spatial, and temporal information on coverage and growth of vegetation.

Methods

Downscaling method

The specific steps of downscaling are as follows (Fig. 2):

  1. 1.

    This article used the remote sensing data of TRMM 3B43 annual precipitation, DEM, and average annual NDVI with three different scales, the resolution of TRMM 3B43 is 0.25° × 0.25°, which equals to 27.5 km, the resolutions of DEM and NDVI are 90 m and 1 km.

  2. 2.

    Correlation coefficient was calculated to verify the accuracy of the TRMM 3B43 precipitation data (Fig. 3).

  3. 3.

    Under the resolution of 0.25°, multiple linear regression models were established based on the annual cumulative precipitation data of TRMM 3B43, latitude and longitude, elevation, and slope of the year of 2014, 2015 and 2016, respectively (Fig. 4).

Fig. 2
figure 2

Technical routine of downscaling method

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Fig. 3
figure 3

Scatter density plot between TRMM precipitation and precipitation simulation based on the downscaling models for a 2014, b 2015, and c 2016

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Fig. 4
figure 4

Images of 1-km resolution after re-sampling and interpolation for a latitude, b longitude, c NDVI, d DEM, e aspect, and f residual

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The model is defined as follows:

$$ Y=a+{bX}_1+{cX}_2+{dX}_3+{eX}_4+{fX}_5 $$
(1)

where Y is the accumulated annual precipitation of a certain year, X1 is the longitude, X2 is the latitude, X3 is the elevation, X4 is the annual max value of NDVI, and X5 is the slope. In addition, a, b, c, d, e, and f are the fitting coefficients of the multiple linear regression models.

  1. 4.

    After performing projection transformation on the TRMM precipitation data, the longitude, latitude, DEM, annual max value of NDVI, and slope in the study area are re-collected at a resolution similar to that of the TRMM precipitation data, which is 0.25° (Fig. 5). Model 1 is simulated with 0.25° spatial resolution. According to the established downscaling regression model, the regression coefficient between the estimated precipitation and TRMM original data is fluctuating around 0.90, implying a high model correlation.

  2. 5.

    The differences value

Fig. 5
figure 5

a Image of TRMM 3B43 under the 0.25° resolution and b image of DEM under the 0.25° resolution

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$$ \triangle ={Y}_{\mathrm{t}}-Y $$
(2)

where, Y is the accumulated annual precipitation of a certain year, and Yt is the annual precipitation data of TRMM over the certain year.

  1. 6.

    Resampling the images with 0.25° spatial resolution to the 1° spatial resolution. Then, the regression coefficient is substituted into the DEM, NDVI, and slope images with a 1 km resolution to obtain high-resolution precipitation estimates (Table 1).

  2. 7.

    The differences value △ with 0.25e resolution is interpolated by using the spline function method and re-collected based on the differences value at 1-km resolution. The estimated precipitation at 1-km resolution is then superimposed with the differences value at 1-km resolution via a raster calculator to obtain high-resolution precipitation data.

Table 1 Brief introduction of experimental data
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Validation

Due to the lack of measurements, we choose the instrument data (Bayanbulak, Yining, Baluntai, Korla) to test. The validation results are based on the comparison between the 3-year observation data from these four stations (there is a total of 12 pairs of data used for validation) by three indexes. The coefficient of determination (R2), the bias (B) and the root mean square error (RMSE) were calculated, which are expressed as

$$ {\displaystyle \begin{array}{c}{R}^2=\Big[\frac{\sum \left(Y-\overline{Y}\right)\left({Y}_t-\overline{Y_t}\right)}{\sqrt{\sum {\left(Y-\overline{Y}\right)}^2}\sqrt{\sum {\left({Y}_t-\overline{Y_t}\right)}^2}}\\ {}B=\sum \frac{Y_2-Y}{Y}\end{array}} $$
(3)
$$ \mathrm{RMSE}=\sqrt{\frac{\sum {\left({Y}_t-Y\right)}^2}{n}} $$
(4)

where, Y is the measured annual precipitation of a certain year, Yt is the annual precipitation data of TRMM over the certain year, and n is the number of data.

Results

Assessment of TRMM 3B43 precipitation data in Tianshan Mountains

Considering the research period and the continuity of the meteorological station data, 16 meteorological stations (including Yining, Zhaosu, Urumqi) were selected to analyze the applicability of TRMM 3B43 precipitation in Chinese Tianshan Mountains. Figure 6(a) shows the regression between the annual average precipitation from the observation stations and TRMM 3B43 values during the period 2014–2016. Figure 6(b) shows the regression between the monthly average data from the observation stations and TRMM values in 2016. The correlation coefficients are 0.72 and 0.69, respectively, demonstrated that high annual and monthly correlations between TRMM precipitation and observation stations data and a high applicability of TRMM 3B43 precipitation data in the Chinese Tianshan Mountains. However, the accuracy of the TRMM 3B43 monthly precipitation data among the different stations remains heterogeneous (Table 2), with large differences value observed in Wenquan, Urumqi, and Kashgar. Accordingly, the uncertainties are observed because of the effects of topography, climate, ocean and continent location, etc. Therefore, a downscaling method is used to improve the accuracy of the TRMM precipitation data.

Fig. 6
figure 6

Comparison between TRMM and measurements of a average precipitation during 2014–2016, b monthly average precipitation of 2016

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Table 2 The models of downscaling
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Downscaling results and validation

With the downscaling model, the high-resolution precipitation data of 1 km from 2014 to 2016 were obtained (Fig. 7). In order to further verify the results of downscaling results, 4 observation stations in the study area were selected, and the measured data, the TRMM 3B43 data and downscaling results, were compared and analyzed (Table 3 and Fig. 8). In general, it can be seen that the differences value between the downscaling results and the measured data is smaller than the raw TRMM3B43 and the measured data; accordingly; the accuracy of the TRMM 3B43 precipitation data is improved.

Fig. 7
figure 7

The high-resolution precipitation data of 1 km from 2014 to 2016

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Table 3 Comparison between annual average precipitation of TRMM and measurements
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Fig. 8
figure 8

a The comparison of TRMM 3B43 and measurements; b the downscaling results and measurements

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The results of validation are demonstrated in Fig. 8 and Table 4, the coefficient of determination (R2) between measurements and TRMM 3B43 increased after downscaling, while the root mean square error (RMSE), and the bias (B) between measurements and TRMM 3B43 are larger than the results of downscaling. The coefficient of determination is increased by 0.03; the bias and the root mean square error reduced by 0.004 and 16.12, respectively. A detailed analysis of the results indicated that TRMM 3B43 precipitation data are underestimated at Bayanbulak station, and the annual precipitation values are generally lower than the observed values. Downscaling results can reduce the level of underestimation and significantly reduce the differences value in TRMM 3B43 precipitation data. The TRMM precipitation data ranges in differences value from 19 to 33.44 mm. After downscaling, the differences value relative to the observed data are substantially reduced and range from 2.02 to approximately 21.41 mm. TRMM 3B43 precipitation data are also underestimated at Balun station, and the differences value range from 21.91 to approximately 53.8 mm. After downscaling, the differences value between the downscaling results and observation data are significantly reduced to 18.3 mm. For the Korla station, TRMM 3B43 precipitation data are overestimated, and the differences value relative to the observation station range from 12.62 to approximately 39.3 mm. After implementing the downscaling method, the differences value is reduced to 11.16~32.07 mm; thus, the models remain to be improved.

Table 4 Comparison between annual precipitation derived from TRMM 3B43, results of downscaling models and measurement (mm)
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For the Yining station, TRMM 3B43 precipitation data show a tendency towards overestimation compared with the observation data. However, after downscaling, the results for certain years are greater than that of the original TRMM 3B43 data. After downscaling, the differences value in 2014 and 2015 are greater than that of the original TRMM 3B43 precipitation data; whereas in 2016, the differences value are significantly smaller than that of the original TRMM 3B43 data and show a reduction from 57.11 to 3.44 mm. A possible reason for these results is that the differences value of TRMM precipitation is relatively small relative to the observation data; thus, the effect of downscaling is not apparent. Conversely, the differences value of TRMM data may be too great. Moreover, the annual precipitation at Yining is higher than that of the other stations, which may have contributed to the poor precision in this area compared with areas that have less precipitation. In addition, during the establishment of the model, the residual differences value was interpolated by using the spline function, and different interpolation methods will have different effects among the stations. Overall, the downscaling model reduced the differences value of the TRMM 3B43 and observation data and improved the accuracy of TRMM 3B43 precipitation data. The precipitation differences value for the recent 3 years shows an improvement of up to 2.02 mm with our downscaling model.

Spatial characteristics of precipitation in the Chinese Tianshan Mountains

According to the downscaling results, the precipitation in the west of middle part of the Chinese Tianshan Mountains is greater than that in the east and the precipitation in the north is greater than that in the south. The total precipitation reduces from the west to the east and increases from the north to the south, which has an obvious vertical distribution characteristics. Precipitation increases with increasing elevation, and the areas with the greatest precipitation are mainly located in high-elevation regions with snow coverage, whereas areas with less precipitation are mainly located along the rim of the north and south slope of Chinese Tianshan Mountains. In addition, precipitation is higher in the west than the east.

Discussion

The downscaling results can reflect annual variations of precipitation. However, this algorithm still has differences value, and possible sources of differences value are discussed as follows.

  1. 1.

    Model. The establishment of the linear regression model and the interpolation of residuals in this study can describe the relationship between precipitation, NDVI, and topography as a linear relationship, certainly, the model can affect the downscaling results and corresponding introduce uncertainty into the downscaling results. In addition, residual differences value is interpolated by using the spline function, and different methods can lead to different results for the stations with different precipitations levels. Moreover, the model does not consider the complex influence of the topography mechanism. The precipitation will increased with the elevation due to the topographical lifting effect on airflow (Jia et al. 2011; Fang et al. 2013), it was also affected by the barrier effect on the air flow and topographical roughness. In addition, the model does not consider the lag period of the relationship between the precipitation and vegetation.

  2. 2.

    Data. The results of Yining show poorer precision, and the annual precipitation of Yining is higher than other stations. Thus, it may indicate that this model has poorer precision in areas with greater precipitation compared with areas with less precipitation. The accuracy of the result of the downscaling is influenced by the algorithm and discontinuity of the TRMM 3B43 data.

  3. 3.

    The downscaling results are related to the elevation. The predicted results reduce the bias in the Baluntai, Bayanbulak, and Korla, which elevation are 2458 m, 1739 m, and 932 m, respectively. The downscaling results shows even greater bias in Yining station, which probably because the evaluation of Yining is only 663 m. But the improvement of precession does not show liner relationship with the evaluation of the station.

  4. 4.

    Although monthly downscaling study was not performed here, it would have provided data and theoretical support to generate more precise precipitation among seasons and months. The limited number of stations in the middle part of the Chinese Tianshan Mountains also hinders our ability to verify the station data and perform an efficient evaluation of the TRMM 3B43 data.

Conclusions

Based on TRMM 3B43 precipitation data, meteorological stations data, DEM, and NDVI of the Chinese Tianshan Mountains during 2014–2016, a multiple linear regression model of downscaling TRMM precipitation data as well as with indexes of longitude, latitude, slope, aspect, DEM, and NDVI, and slope data is established. A spatial downscaling process is performed on the precipitation data to obtain spatial distribution in the Chinese Tianshan Mountains with a 1-km spatial resolution. The results are verified using observation data from the meteorological stations. The conclusions are as follows:

  1. 1.

    TRMM data are underestimated at Bayanbulak station and Balun station, and the annual precipitation is generally lower than the observed precipitation. The downscaling model can reduce the underestimation, and it also can reduce the differences value in the TRMM data. TRMM data at Yining station and Korla station display overestimation trend compared with the observation data. After downscaling, the differences value at Korla station is reduced significantly. However, at Yining station, the downscaling process improves the precision for the 2016 data but increases the differences value in 2014 and 2015 compared with the corresponding TRMM data.

  2. 2.

    The model fit well the area of high elevation and moderate precipitation. And the downscaling model improves the resolution of the original precipitation data of TRMM 3B43, making the downscaling results more clearly and specifically depict the spatial distribution characteristics of precipitation in the middle part of Chinese Tianshan Mountains. Its main feature is that the western part is more than the eastern part, and the north is more than that on the south.

  3. 3.

    TRMM data can be used for the study of precipitation and water resources allocation in the Chinese Tianshan Mountains. In the mountainous areas, topography has a great impact on precipitation, so the impact of slope, aspect, altitude, and vegetation should be considered when downscaling precipitation data. The difference value between the downscaling results and the meteorological station data is significantly reduced. The accuracy is significantly improved compared with the original TRMM 3B43 precipitation data. Therefore, the downscaling model constructed in this paper can be used for the precipitation downscaling study in the Chinese Tianshan Mountains and can provide reference for mountain precipitation downscaling in other regions. There is still large differences value in the downscaling results of some stations in some years, and there are many possible reasons, which are related to the precision of raw TRMM 3B43 data; we were unable to exclude the mutation value due to the short duration of the study.