Study area

This study focused on the eastern Tibetan Plateau and the surrounding areas, with an area of approximately 1.1 million km², ranging from 25.5°N to 37.6°N and 86.4°E to 105.5°E (Figure 1). The special topography of the Tibetan Plateau results in a complicated climatic system that is different from that of surrounding areas. The eastern part of this region is affected by the East Asian monsoon, but the precipitation in the area is not very high because the moist airstream from the sea travels a long distance and is obstructed by the Hengduan Mountains. Another source of precipitation is the Indian monsoon from the Indian Ocean. Most of the moist airstream is obstructed and turned into large-scale precipitation by the Himalayas, but some of the air travels along the Brahmaputra and brings flush precipitation to the middle of the study area. The western region is drier because neither the East Asian monsoon nor the Indian monsoon can reach it. The temporal distribution of precipitation over the Tibetan Plateau shows apparent seasonal characteristics, with most precipitation coming between May and September (Shen et al 2011).

FIGURE 1

DEM of the study area and location of the 188 rain gauges used in this study.

Data

Ground observation from rain gauges

The ground observations used in the study were measured with 188 rain gauges managed by the Institute of Tibetan Plateau Atmospheric and Environmental Science. The maximum, minimum, and mean values and the variance in the precipitation for each month are shown in Table 1. These rain gauges are located in the middle and eastern parts of the Tibetan Plateau with elevations ranging from 2437 to 4728 m (as shown in Figure 1). The number of rain gauges is too limited to accurately monitor the precipitation over this vast plateau, but the configuration of these rain gauges is relatively even. In this study, these rain gauge observations were separated into a training dataset and a testing dataset: 133 rain gauges (labeled as circles in Figure 1) were randomly selected, and the observations from these rain gauges were used to estimate the precipitation over the Tibetan Plateau with the FETCH_OCK model, while the observations from the remaining 55 rain gauges (labeled as rectangles in Figure 1) were used to assess the performance of the model in this study.

TABLE 1

Maximum (max) precipitation, minimum (min) precipitation, average (mean) precipitation, and variance of precipitation observed by 188 rain gauges between 2005 and 2009.

OCK interpolation

OCK is a multivariate interpolation model derived from ordinary kriging (Li and Shao 2010). Apart from the sample data (rain gauge observation in this study), 1 or more types of relative spatial data such as DEM were also introduced into the interpolation process as auxiliary variables (also known as covariants). The covariants usually have a close relationship to the distribution of precipitation. Several studies have shown that OCK with DEM as a covariant can simulate more precisely than other spatial interpolation models. The cokriging precipitation estimating model with only 1 covariant according to Goovaerts (2000) is shown in Equation 1:

where Z_ck(u) is the precipitation estimate result of cokriging at an unsampled location u; n(u) is the number of rain gauges used to simulate rainfall depth at location u; Z(u_a) is the value of the rain gauge observations at location u_a around location u; y(u) is the value of DEM at location u; m_y and m_z are the global means of rain gauge observation and DEM, respectively; and l_a(u) and l(u) are the interpolation weights, which were calculated by solving Equation 2:

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where l(u) and m(u) are Lagrange parameters accounting for the constraints on the weights; g_zz(h) and g_yy(h) are the covariance functions of the rain gauge and DEM, respectively; and g_zy is the cross-semivariogram value between rain gauge observations and DEM.

The g_zz function is calculated by Equation 3:

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where z(u_a) is the rain gauge observation and N(h) is the distance between each point pair.

The g_yy function is calculated by Equation 4:

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where y(u_a) is the value of elevation and N(h) is the distance between each point pair.

The g_zy value is calculated by Equation 5:

where z(u_a) and y(u_a) are the rain gauge observation and DEM, respectively.

In the interpolation process of OCK, self-correlation between the point data and the covariant was considered. Furthermore, the model considers cross-correlation between the covariant and the sample collection, which plays an important role in improving the precision of ordinary kriging. If the cross-correlation between the precipitation and the covariant is strong, the spatial continuity patterns between the precipitation and the covariant are similar, indicating that the covariant has a great influence on the interpolation. However, if there is low or no cross-correlation between the sample collection and the covariant, the effect of the covariant is negligible and OCK can be treated as ordinary kriging.

The FETCH_OCK model

Although OCK can derive unbiased estimates of regionalized variables at unsampled points from the values of the surrounding stations, this model has significant drawbacks when it is used to simulate the spatial pattern of precipitation over mountainous areas. Precipitation is a complicated and discontinuous physical process affected by local atmospheric circulation, topographical local relief, land cover, and many other factors. These factors usually lead to obvious small-scale spatial variability in precipitation. Unfortunately, small-scale spatial variability of precipitation cannot be presented by OCK interpolation for 2 reasons. First, a dense and well-configured rain gauge network is essential to monitor the small-scale spatial variability of precipitation comprehensively, but the rain gauge network in remote and mountainous areas are usually sparse and located unevenly. Second, OCK fits the semivariogram with minimum mean-square-error–based methods, but all fitted curves generated by these methods are too smooth to present the extreme spatial variability given by the semivariogram. This shortcoming of OCK merits significant attention on the Tibetan Plateau, where the rain gauge network is sparse and the spatial pattern of precipitation is severely disturbed by the complicated underlying surface (Olea and Pawlowsky 1996; Yamamoto 2005).

Microwave remote sensing is a promising way to overcome the drawbacks of OCK. Compared with the limited coverage of the rain gauge network, the microwave meteorological satellites network can cover the whole Tibetan Plateau with high temporal resolution (3 hours). Another important advantage of microwave remote sensing is that microwave radiation can break through the clouds and provide the distribution of the precipitation particles, such as big raindrops and ice particles inside the clouds, so the microwave-based satellite precipitation datasets have a direct physical relationship with the real spatial pattern of precipitation. Based on the previous discussion, we assumed that the small-scale spatial variability of precipitation over the Tibetan Plateau can be observed by microwave remote sensing and reflected by the microwave-based satellite precipitation dataset. The FETCH_OCK model, which is aimed at correcting the smoothing effect of OCK and providing a more accurate precipitation dataset over the Tibetan Plateau, was established based on this assumption. Three steps are presented to describe the FETCH_OCK algorithm.

Step 1

The monthly precipitation measured by 133 rain gauges was interpolated by OCK, with DEM as a covariant, using Equations 1–{ label needed for disp-formula[@id='i0276-4741-33-4-424-e02'] }{ label needed for disp-formula[@id='i0276-4741-33-4-424-e03'] }{ label needed for disp-formula[@id='i0276-4741-33-4-424-e04'] }5 and then resampled to 0.25° × 0.25°, which is the same as CMORPH. According to the semivariogram of rain gauges calculated by Equation 3, the semivariogram of DEM calculated by Equation 4, the cross-semivariogram between the rain gauge and DEM calculated by Equation 5, and the spherical model (Equation 6) were selected to fit each variogram (Goovaerts 2000). Equation 6 is as follows:

where a is the range of the variograms and h is the distance of the point data pairs.

Step 2

The small-scale spatial variability in the monthly CMORPH satellite precipitation dataset was extracted by calculating a parameter we named FETCH, because it was developed from the Fetch parameter proposed by Yin et al (2008). Yin et al's Fetch parameter is used to represent the spatial variability of an image; it is calculated by subtracting the smoothed image from the original image using a low-pass filter. In this study, Yin et al's Fetch parameter was modified by dividing their Fetch with the smoothed image to extract the spatial variability of CMORPH satellite precipitation datasets in the form of a ratio. This modified parameter was renamed FETCH.

The FETCH parameter was calculated using a 3-step algorithm. First, CMORPH was smoothed by a 3 × 3 moving window filter, which means the value of a grid in original image was substituted with the average value of the surrounding grids. Second, the smoothed CMORPH was subtracted from the original CMORPH. Finally, FETCH calculated with the result of step 2 was divided by the smoothed CMORPH. The algorithm was described by Equation 7:

where FETCH(u) is the value of FETCH in grid u, T(u) is the value of CMORPH in grid u, and T(i) is the value of the grids around grid u. The negative values of FETCH indicate that the precipitation of this grid in CMORPH is lower than that of the surrounding grids, and vice versa.

Step 3

The result of OCK (termed OCK_DEM) was corrected by FETCH following Equation 8. As shown in this equation, the grid in the result of OCK was multiplied by FETCH of the corresponding grids, and then the result was added to the original value of OCK.

Here, FC(u) is the result of FETCH_OCK in grid u, FETCH(u) is the value of FETCH in grid u, and T_OCK(u) is the result of OCK with DEM as a covariant.

Precision evaluation

The ground observations from 55 rain gauges that were not used in the training process were used to assess the performance of the models in the study. Four comparison criteria were calculated: mean absolute error (MAE), root-mean-square error (RMSE), coefficients of determination (R²), and sum of squares of residuals (SSE). These criteria were calculated by Equations 9–{ label needed for disp-formula[@id='i0276-4741-33-4-424-e10'] }{ label needed for disp-formula[@id='i0276-4741-33-4-424-e11'] }12, respectively:

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where Y_k is the observation measured by rain gauge k, O_k is the precipitation estimated by a model at the location of rain gauge k, is the mean value of all rain gauge observations and the precipitation estimate value, and is the mean value of the precipitation at all rain gauge locations.

The spatial pattern of OCK, FETCH, and FETCH_OCK

Figure 2 shows the precipitation dataset estimated by OCK, with DEM as a covariant (August 2007 is taken as an example). Although the complicated topography information was introduced into the interpolation process, the spatial distribution of precipitation estimated by OCK presented an evident smoothing effect. For example, in the Himalayas, where the Indian monsoon is seriously disturbed by the huge mountains, there should be a dramatic fluctuation between high and low precipitation on the southeast-facing and northwest-facing slopes for mountain ranges across the Tibetan Plateau, according to the study by Yin et al (2008). But the spatial pattern of the precipitation estimated by OCK still presents a continuous surface, which cannot represent the thermal and dynamic forcing mechanisms of the topography.

FIGURE 2

Monthly precipitation (in millimeters) over the south Tibetan Plateau in August 2007 as calculated by the OCK interpolation with DEM as a covariant.

Figure 3 presents the result of FETCH in August 2007, as derived from CMORPH satellite data. The circles and the rectangles in this figure represented grids with FETCH above 0.2 and below −0.2, respectively. They indicated that the precipitation of CMORPH in these grids showed a distinct decrease (when FETCH was negative) or increase (when FETCH was positive) compared with surrounding grids. As shown in Figure 3, most of these labeled grids are located in the western part of the study area and in the Himalayas, where the underlying surface is complicated.

FIGURE 3

Spatial distribution of FETCH in August 2007 on a 0.25° latitude–longitude grid. The circles represent the grid with FETCH below −0.2, while the rectangles represent the grid above 0.2.

Figure 4 shows the spatial pattern of the precipitation estimated by the FETCH_OCK model in August 2007. It can be observed that in the middle and eastern parts affected by the East Asian monsoon, the spatial pattern of FETCH_OCK is similar to OCK, because most of the values of FETCH in these regions are relatively low. This indicates that the underlying surface of these regions cannot disturb the spatial pattern of precipitation seriously. But in the western and southern parts of the study area, the precipitation estimated by FETCH_OCK presents a seriously discontinuous surface compared with the result of OCK, because the spatial pattern of precipitation estimated by OCK was corrected by the extreme spatial variability of precipitation extracted from CMORPH satellite precipitation datasets. Furthermore, the ranges of the precipitation estimated by FETCH_OCK are closer to the rain gauge observation than are the ranges of OCK. Table 2 showed the maximum and minimum precipitation estimated by OCK and FETCH_OCK at the locations of the 133 rain gauges. The maximum precipitation values of OCK_DEM and FETCH_OCK were both underestimated, while the minimum values were overestimated. By comparison, the maximum and the minimum values of FETCH_OCK were closer to the range of rain gauge measurements than those of OCK_DEM in each month.

FIGURE 4

Monthly precipitation (in millimeters) dataset on a 0.25° latitude–longitude grid over the Tibetan Plateau in August 2007 as estimated by the FETCH_OCK model.

TABLE 2

Maximum and minimum values of OCK_DEM and FETCH_OCK at the locations of the 188 rain gauges.

Validation and comparison with other precipitation datasets

In this section, the observations measured by independent rain gauges were used to validate the results of FETCH_OCK models. We first investigated whether FETCH_OCK shows obvious improvement in the input precipitation datasets (OCK and CMORPH). Performance of FETCH_OCK was further assessed by comparing it with 2 widely used precipitation datasets: UK and TRMM 3B43.

Figure 5A–D show the R², MAE, RMSE, and SSE, respectively, for summer precipitation (June to August) estimated by CMORPH, OCK, and FETCH_OCK between 2005 and 2009. It can be seen from Figure 5A that R² in the FETCH_OCK model was always above 0.5 and higher than in the other 2 precipitation datasets. In some months, the value of R² can reach up to 0.82, which indicates that the precipitation predicted by FETCH_OCK correlated well with the rain gauge observation. The RMSE of FETCH_OCK decreased to 26.76∼66.77, compared with CMORPH (36.33∼89.58) and OCK (29.22∼70.56). The same decrease in MAE and SSE can be observed in Figure 5C and D. The 4 evaluation criteria indicated that FETCH_OCK presented substantial improvement in the precipitation estimate over the Tibetan Plateau when compared with OCK and CMORPH.

FIGURE 5

R² (A), MAE (B), RMSE (C), and SSE (D) of the summer precipitation (June to August) as estimated by CMORPH, OCK, and FETCH_OCK between 2005 and 2009.

The R², MAE, RMSE, and SSE, respectively, of FETCH, UK, and TRMM 3B43 are shown in Figure 6A–D. UK is an interpolation method that combines regression and kriging by treating these as 2 separate, consecutive steps. In this model, the secondary information is used to derive the local mean of the primary attribute and then to perform simple kriging on the corresponding residuals (Brus and Heuvelink 2007). UK was used to estimate the precipitation, with elevation as a covariant, and showed better performance than other interpolation methods in many studies (Lloyd 2005; Bostan et al 2012). The unsampled point u was estimated by observations around u_i following Equation 13:

where Z_uk(u) is the prediction at location u, a₀ is the estimated intercept, a_k are the estimated regression model coefficients, X_k(u) are the values of independent variables, b_i are the simple kriging weights derived from the spatial dependence structure of the residual, ε(u_i) is the (observed) regression residual at location u_i, p is the number of the rain gauge observations, and n is the number of the observations around u.

FIGURE 6

R² (A), MAE (B), RMSE (C), and SSE (D) of the summer precipitation (June to August) as estimated by the TRMM 3B43, UK, and FETCH_OCK models between 2005 and 2009.

It can be observed from Figure 6 that FETCH_OCK presented a higher value for R², as well as lower RMSE, SSE, and MAE, than UK with DEM as a covariant in all months, which indicates that FETCH_OCK performed better than UK in estimating summer precipitation over the Tibetan Plateau. In comparison with TRMM 3B43, FETCH_OCK performed better in most months, except in July 2005 and 2009, when FETCH_OCK showed lower or similar R² and higher RMSE, SSE, and MAE. However, even in these months, the R² of FETCH_OCK can reach as much as 0.53 (July 2005) and 0.81 (July 2009), which indicated that although the performance of FETCH_OCK is not as good as TRMM 3B43, FETCH_OCK provided a reasonable spatial pattern of precipitation over the Tibetan Plateau in the 2 months.