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Mathematical Derivation
The dataset has to be organized in three dimensions of (1) time with a regular time interval (e.g. monthly or annual), (2) space with regular spatial units where all the grids are re-organized in a new dimension from the original latitude-longitude grids, (3) ensemble with different ensemble members regarded as the third dimension. Thus, the dataset array can be reformed as Z = [zi jk] (2.1).
with i-th time step (i = 1, 2, . . . , m), j-th grid (j = 1, 2, . . . , n), and k-th ensemble member or ensemble model (k = 1, 2, . . . , l).
We define the three dimensions as time, space and ensemble dimension and the means for these three dimensions are called temporal mean, spatial mean and ensemble mean, respectively. The corresponding variances are named time variance, space variance and ensemble variance, respectively. The grand mean (μ), grand variance across time, space and ensemble models (!2) as well as the total sum of squares (SST) are defined as. μ = ’m i=1 ’n j=1 ’l k=1 zi jk/(mnl).
Study area and data descriptions
China is large in its area, and different climate types are encountered in the mainland (Kottek et al. 2006). To facilitate the comparisons and analysis that have spatial variations, ten different regions are defined in Figure 2.2 as the (1) Songhua River Basin, (2) Liao River Basin, (3) Hai River Basin, (4) Yellow River Basin, (5) Huai River Basin, (6) Yangtze River Basin, (7) Southeast China, (8) South China, (9) Southwest China, (10) Northwest China.
The entire Chinese mainland is numbered as the 11st region. Most of the regions are natural river basins, and this definition is better in water resources analysis than definitions using longitude-latitude grids or that are based on administrative regions.
As shown in Table 2.1, thirteen precipitation datasets from different sources are collected for comparison. All these datasets are categorized into three groups, i.e., gauge-based products, merged products and General Circulation Models (GCMs). The gauge-based products only rely on the gauge measurements, but the collected gauges and algorithms to generate the precipitation map are different among different products. CMA (China Meteorological Administration) dataset uses the densest gauges and probably has the best quality to capture the spatiotemporal variations of the precipitation. CMA is therefore chosen as the reference datasets for comparisons, and it is excluded when estimating the ensemble means of the gauge-based products. The merged precipitation products rely on databases from many various sources including satellite remote sensing, radar radiation or re-analysis dataset. These datasets are also assimilated with gauge observations to correct potential biases. The GCMs precipitation is modeled without correction from any measurements. The difference among GCMs is therefore a result of the model differences (e.g., initial conditions, model algorithms, numerical simulations). They also have a different synoptic variability as they are not constrained to follow a specific trajectory in the manifold of all possible climatic solutions. There are more than 20 datasets of GCMs, while only four are randomly taken to match the number of gauge-based products and merged products. All the datasets have been interpolated to 0.5o spatial resolution. The overlap time span of all the datasets is from 1979 to 2005 for the maximum coverage of all products. Four different products are included in each precipitation group, which can explain more than 80% of the uncertainties when much more models are used. The details of the explanation is shown in the appendix A.
Uncertainty between different precipitation groups
The ensemble means of the long-term annual precipitation (1979-2005) at each grid are estimated and mapped as Figure 2.3. The ensemble mean of the gauge-based products has excluded the CMA dataset. The ensemble means for the precipitation in three groups are obtained by averaging the datasets in corresponding group. The annual precipitation is 589.8 mm/yr (1.6 mm/day) in the China mainland with CMA data (Table 2.2). The absolute bias in other gauge-based products, merged products and GCM is -4.1, 63.1, 232.0 mm/yr (with the bias as -0.7%, +20.4% and +41.3%) respectively. The spatial pattern of the annual precipitation shows a decreasing trend from the southeast China (>1600 mm/yr) to the northwest China (<400 mm/yr) and all the ensemble means for the three groups capture the spatial gradient.
However, because of the deviation of precipitation in different groups, the land area with a certain magnitude of annual precipitation can change and shift in its locations. The annual precipitation is an important factor that determines the climate type in the Köppen-Geiger climate classification system (Kottek et al. 2006). For instance, 2.66⇥106km2 (28.2% of the China mainland area) has annual precipitation more than 800 mm/yr in CMA dataset, which can be categorized as the humid region (Table 2.2). 3.88⇥106km2 has annual precipitation less than 400 mm/yr, belonging to the dry area. 2.89⇥106km2 locates in the transition area, with annual precipitation between 400 and 800 mm/yr.
Variations in the time and space dimensions
The precipitation varies in time and space. However, it is averaged either in the time dimension to compare the spatial patterns (Figure 2.3) or in space dimension to compare the temporal variations (Figure 2.6). The deviations in the time and space dimensions are therefore very rarely compared. Herein, the standard deviation of the temporal and spatial variations in annual precipitation datasets are compared in Figure 2.7 in ten regions and the The gauge-based products provide similar annual regional precipitation to CMA over the China mainland and ten specific regions except for the region 7-southeast China (Figure 2.7-g). The regional precipitation is larger in merged products than that of observations. The spatial variations are the same for the GCMs, while the magnitude of the deviation in GCMs is even larger except in the region 8-south China (Figure 2.7-h). These results indicate the reduced ability of merged products and GCMs in reproducing the total value of the annualp recipitation.
Regarding the variations in time and space dimensions, the 3-Hai River basin and 7- southeast China have the comparable values of temporal standard deviation (t.std) and spatial standard deviation (s.std). It is mainly because these two regions are relatively small so that the spatial heterogeneity is not strong in a given climate type. The t.std is also large in these regions (Figure 2.6). So that the t.std is similar to s.std. Larger s.std is found in the regions of 1-Songhua River basin, 2-Liao River basin, 5-Huai River basin and 8-South China. The area of these regions is larger than the previous two basins, and the spatial heterogeneity is therefore larger than that in the previous two basins. For the other four regions (i.e., 4-Yellow River basin, 6-Yangtze River basin, 9-southwest China, 10-northwest China) and the China mainland, the spatial variation is significantly larger than the variations in the time dimension.
The main reason is that these large regions span areas with different climate types where the annual precipitation may be significantly different in the annual means. For example, in the CMA dataset, the annual precipitation over China mainland is 592.6±25.0 mm/yr in difference years, while it is 592.6±494.5 mm/yr at different grids in China. The very small ratio of the t.std to s.std (25.0/494.5=0.05) indicates a higher reliability of annual regional precipitation in a specific year than the reliability of the annual precipitation at a specific grid point.
Variances in three dimensions
The standard deviations in either the space dimension or the time dimension in Figure 2.7 are estimated based on the ensemble means of the same precipitation group. The differences among datasets within that group (used to build the ensemble mean) are therefore not considered. On the other hand, although the standard deviation among the ensemble members can be compared with either the spatial means or the temporal means in Figure 2.5 and 2.6, it cannot evaluate the impact of ensemble variations on both the temporal dimension and spatial dimension together. It is therefore more difficult to compare the variation among the datasets together with the spatial variation and temporal variation by current approaches. A method which can integrate the variations together in the ensemble dimension, the temporal dimension and the spatial dimension is therefore needed for their comparisons.
As introduced in the methodology section, the ensemble variance can be estimated by the proposed three-dimensional partitioning approach. The input annual precipitation to the approach is organized into three dimensions as (1) time, 27 years from 1979 to 2005, (2) space, the number of 0.5o grids in a specific region and (3) ensemble, the number of the models in a same precipitation groups (4 models in all three groups).
The grand variance and the variances in three different dimensions (i.e., time, space and ensemble) for all the regions are mapped in Figure 2.8. It is similar for data groups of gaugebased products and the merged products for the grand variance (total value of the variance for all three dimensions, Figure 2.8-a,b,c), while the grand variance in GCMs is approximating twice the values of the grand variance in regions 9-south China and 10-southwest China. The differences are mainly constituted by the space variance and ensemble variance (Figure 2.8-i,l).
The time variance (Vt ) is the smallest of all three variance proportions, and there are very little differences of Vt in the north China (Figure 2.8-d,e,f). Vt in the gauge-based products is higher than that in the merged products and GCMs in regions 8-southeast China and 9-south China, indicating a relatively strong temporal variation in the annual precipitation series. For the space variance (Vs), similar patterns are found in the gauge-based products and merged products (Figure 2.8-g,h), the 7-Yangtze River basin and 9-southwest China have the largest Vs because the precipitation significantly varies in space in these two regions. Vs is higher in the precipitation of GCMs especially in the 9-southwest China, indicating the strong spatial heterogeneity in the GCM models over the Himalayas (Figure 2.8-i). The ensemble variance (Ve) is relatively small in most of the regions in gauge-based products (Figure 2.8-j), with the highest Ve occuring in 9-southwest China. It indicates that the model variation between regions in merged products as well as in the GCMs for the regions in north China, while the intra-ensemble variations are large in the south especially the 9-southewest China and 8-south China in the GCMs (Figure 2.8-k,l).
In conclusion, the grand variance and variances in three different dimensions are generally larger in the dataset group consisting in GCMs. The variations for the gauge-based products and merged products are similar in values and spatial distribution. However, the statistics only show the total variances without consideration of the absolute regional means. The deviations which are estimated as the ratio of the square root of the variance to the mean (i.e., U, Ut , Us, Ue) should be evaluated to eliminate the systemic effect of the average means. Moreover, it is not easy to capture how the three variances vary with each other from Figure 2.8. The normalized variance proportion in time, space and ensemble dimensions Pt , Ps, Pe are therefore analyzed as well in the next sections.
Variance proportions in three dimensions
All of the variance proportions are normalized so that the comparison between variances in different dimensions becomes easy. As shown in Figure 2.9, the Pt is in general the smallest among the three variances and the Ps is the largest, which agrees with the standard deviation comparisons in Figure 2.7. The Ps is especially large in the 7-Yangtze River basin and 10-northwest China because the area is the largest and they span different climate zones (Figure 2.9-d,e,f). The ensemble variance Pe is smaller than the Pt in the observation dataset group in the east China (Figure 2.9-g), which is probably because the gauge-based products are based on similar sets of observations to some degree and the orographic effect is not obvious in the east so that interpolation will not induce large uncertainties in the precipitation maps. Pe is generally lower than the Ps while an exception is found for the GCMs in the 8-southern China (Figure 2.9-i), indicating significant variations in different GCM models in estimating the precipitation. The model deficiency to represent the monsoonal flows in GCMs may result in the large differences.
Table of contents :
1 Introduction
1.1 Scientific context
1.2 Literature review
1.3 Scientific questions and objectives
1.4 Plan of the thesis
2 Assessment of the uncertainty in precipitation
2.1 Introduction
2.2 Methodology and datasets
2.3 Uncertainty in precipitation products
2.4 Variances in precipitation products
2.5 Uncertainty and metric comparisons
2.6 Discussion and Conclusion
3 An ORCHIDEE-Budyko framework to attribute the discharge bias
3.1 Introduction
3.2 Study area and hydro-meteorological characteristics
3.3 Data and Models
3.4 Results and discussion
3.5 Conclusions
4 Human impact on river discharge in China regions – a review
4.1 Introduction
4.2 How humans change river discharge
4.3 Quantification methodologies of the human impacts
4.4 Comparisons of human impacts to other uncertainties
4.5 Summary
5 Conclusions and perspectives
5.1 Conclusions
5.2 Perspectives
A Submitted paper II
A.1 Introduction
A.2 Methodology
A.3 Model application
A.4 Discussion and conclusion
B List of abbreviations
