A Comparison of Two Downscaling Methods for Precipitation in China

Journal of Geoscience and Environment Protection, 2015, *, ** Published Online **** 2015 in SciRes. http://www.scirp.org/journal/ gep http://dx.doi.org/10.4236/ gep .201 5 .*****

A comparison of two downscaling methods for precipitation in China

Na Zhao, Tian-Xiang Yue, Xun Zhou State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, 100101 Beijing, China E-mail: [email protected]

Received **** 2015

Copyright © 2015 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

Abstract In most cases climate change projections from General Circulation Models (GCM) and Regional Climate Models (RCM) cannot be directly applied to climate change impact studies, and downscaling is therefore needed. A large number of statistical downscaling methods exist but no clear recommendations exist of which methods are more appropriate, depending on the application. This paper compares two different statistical downscaling methods, Presim1 and Presim2, using the Coupled Model Intercomparison Project Phase 5 (CMIP5) datasets. Both methods include two steps but the major difference between them is how the CMIP5 dataset and the station data used. The downscaled precipitation data are validated with obser- vations through China and Jiangxi province from 1976 to 2005. Results show that GCMs cannot be used directly in climate change impact studies. In China, the second method Presim2 which establishes regression model based on the station data has a tendency to overestimate or underestimate the real values. The accuracy of Presim1 is much better than Presim2 based on mean absolute error (MAE), mean relative error (MRE) and root mean square error (RMSE). Presim1fuses the mode data and station data effectively. Results also show the importance of the meteorological station data in the process of residual modification.

Keywords Global climate models, Statistical downscaling method, Geographical Weighted Regression method (GWR), High Accuracy Surface Modeling (HASM), precipitation, China

1. Introduction Precipitation as a fundamental component of the global water cycle, is a key parameter of ecology, hydrology and meteorology [1, 2, 3]. Understanding and quantifying the spatial variability of precipitation are of key importance in hydrological studies as precipitation drives most hydrological, environmental and agricultural processes. However, strong precipitation gradients over short distance are difficult to capture with point measure-

How to cite this paper: Na Zhao, Tian-Xiang Yue and Xun Zhou (2015) A comparison of two downscaling methods for precipitation in China. *********, *, **-**. http://dx.doi.org/10.4236/ gep .201 5 .***** N. ZHAO, T.X. YUE, X. ZHOU

ments from meteorological stations. Stations are generally located in areas which are readily accessible. And it is usually low and insufficient for the use of conventional spatial interpolation techniques [4, 5]. In recent years, the development of remote sensing and geographic information technology has presented us with new methods of precipitation observation [6]. Satellite precipitation data have been widely evaluated with a better performance [7] and used for many applications such as hydrological modeling [8, 9, 10], flood prediction [11], rainfall erosivity estimation [12] and climatological studies [13]. But studies show that different remote sensing data have different performance in China [14, 15]. Moreover, remote sensing offers data only of recent years. In the World Climate Research Programme (WCRP), different global climate models (GCMs) participating in the Coupled Model Inter-comparison Project Phase 5(CMIP5). The Coupled Model Intercomparison Project Phase 5 (CMIP5) datasets have been used for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (AR5).These simulations of GCMs have demonstrated the ability to generally replicate the precipitation trend over the second half of the twentieth century, and can offer precipitation in a longer time scale. However, GCMs have so far been too coarse to resolve this geographically well-defined region. One has to therefore resort to either statistical or dynamical methods to downscale the large-scale information to the regional scale and to resolve the important geographical induced features. A number of studies have been carried out to create a connection between climate change at the large scale and at the regional scale. The most straightforward approach is linear or more sophisticated methods of interpolation between large-scale grid points closest to the region to infer the regional scale. This method has attracted a lot of criticism, since it is felt that the model reso - lution is too coarse and the model performance is too poor to allow for interpolation of the results. To overcome the problems with direct interpolation, the approach termed downscaling can be pursued. This approach is based on the understanding that the large-scale information provided by standard coarse-grid GCMs may be postpro- cessed together with the regional information to specify the regional details of the present climate and its sensi - tivity to changes in atmospheric composition or other external anomalies. Statistical downscaling method is widely undertaken because it is easy and fast to apply [16, 17]. Statistical downscaling is a two-step process consisting of i) the development of statistical relationships between local climate variables and large-scale pre- dictors and ii) the application of such relationships to the output of GCM experiments to simulate local climate characteristic in the future. Here, we present two downscaling methods and compare them to give the optimal one for China. We use the meteorological site information over China to downscale the simulations of CMIP5 output results. The statistical downscaling methods used here involves two steps: 1) determining a local linear model by Geographical Weighted Regression method (GWR) for every location in the prediction domain, 2) using the High Accuracy Surface Modeling method (HASM) to modify the residual produced by the first step. Then, we use the separate dataset in Jiangxi province and 10% of the data from national scale to validate the results. And at last, a conclusion is given in the final section.

2. Study Area and Data China, covering an area of about 960,0000km2, is the third largest country on earth, and China’s topography varies enormously from high mountainous regions to inhospitable desert zones and flat, fertile plains. It is a predominantly mountainous country with a very distinct structural pattern. The extremely varied landforms of China affect the climate conditions in various ways. For precipitation, mountains effectively control the flow and passage of air masses, which may be blocked, diverted or channeled. In addition to the huge territory, ex - treme air distances and latitudinal and longitudinal distances also represent important controlling factors where it comes to climate. Because of its vast area and complex terrain, there are significant differences in precipitation. China is under the influence of the winter monsoon from October to March, during the dry season. The summer monsoon prevails from June to August when precipitation is plentiful. April, May and September are transitional months between the dry and wet seasons, resulting in remarkably variable precipitation for the whole region [18].

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Figure 1. Spatial distribution of the meteorological network in China. We used the World Climate Research Programme's (WCRP's) Coupled Model Intercomparison Project phase 5 (CMIP5) multi-model dataset and precipitation data from 752 stations for the period 1976-2005 (Figure 1). We chose 10% of the total sampled points to verify test results and withheld from the downscaling calculations. We also use the meteorological stations in Jiangxi province to validate the results. The main geomorphologic characteristics of China and weather types affecting the country are such that the stations are representative and cover almost all climatic regions expect the mountainous areas with a polar climate.

3. Method The statistical downscaling method used in this study can be summarized as,

Presim  Pr edownscale  Pr eres (1) where, Presim is the final result, Pr edownscale is the downscaling result and will be obtained by the GWR

method. Preres is the residual and will be interpolated by HASM. The two downscaling methods are different

according to the data used in Pr edownscale , and thus in Preres . We denote the result of the first method is

Presim1 and the second is Presim2 . For Presim1 , we use CMIP5 output to get Pr edownscale1 , and employ station

data to modify the residual to obtain Pr eres1 . While for Presim2 , we use meteorological information to produce

Pr edownscale2 , and employ the results of CMIP5 to modify the residual to obtain Pr eres2 [19].

3.1. Local Regression Method Due to the large gradients in precipitation means and variances in China, the best method of calculating precipitation is to transform the original data first. We first normalize the precipitation data to limit the extreme value,

5 N. ZHAO, T.X. YUE, X. ZHOU

Prei Pr ei = (2) max{Pr ei, i= 1,..., n}

where, Pr e is the CMIP5 simulation value in the first method or the station data in the second method, is i Pr ei the transformed data, is the number of grids of CMIP5 results or the number of stations. n Then we carry Box-Cox transform of , which can give a more normal distribution and/or improved pre- Pr ei dictions [20, 21]. The formulation of this transformation is,

ln Prei ,d = 0 d Pr ei = (3) Prei - 1 ,d 0 d

where, Pr ei is the Box-Cox transformed data and d is a suitable parameter, which is selected to make Pr ei obey normal distribution and thus satisfy the assumption of GWR method [22]. In this paper, d = 0.4 in the first method and d = 0.48 in the second method. Studies have shown that this process avoids negative values in the results and is necessary for precipitation interpolation [23]. Unlike the ordinary linear regression model, GWR [24,25] enables the spatial drift of regression parameters to be identified, estimated and mapped, which is especially important for characterizing highly variable precipitation within China. The GWR method has been successfully used in precipitation research [26] and the formulation of GWR can be written as N

Predownscale= d0,0 ( x i , y j ) + a i , j d i , j ( x i , y j ) (4) i, j= 1 Pre is the downscaling value of (i , j ) grid-box in the finer scale; d x, y is the intercept; a is downscale 0,0 ( i j ) i, j

the explanatory variable and di, j( x i, y j ) is the corresponding coefficient which is a function of the position.

xi, y i are the longitude and latitude, respectively. We select the independent variables from latitude, longitude, elevation, impact coefficient of aspect and sky view factor according to the value of the adjust R2 in GWR. And in this research, the most influence factors are latitude, longitude, elevation and impact coefficient of aspect with R2 is equal to 0.92 for the first method and 0.91 for the second method.

3.2. HASM As an innovative method [27], HASM is based on the fundamental theorem of surfaces which ensures that a surface is uniquely defined by its first and second fundamental coefficients. The equation of HASM is the follow- ing symmetric positive definite linear system [28], Wx n + 1 = v n (5) where W= AT A+ B T B + C T C + l 2 S T S , v= AT d + B T q + C T p + l 2 S T k , l is a suitable parameter. The preconditioned conjugate gradient method can be used to solve Equation (5) and the solution x is the simulated

value of the residual Preres in Equation (1).

4. Results and Discussion

We fist compare two methods in Table 1. Prems is the CMIP5 output. Three indices, mean absolute error (MAE) , mean relative error (MRE) and root mean square error (RMSE), were calculated from the station value and downscaling value at each validation sample site. The formulations of these indexes are:

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Table 1. Comparison of two downscaling methods. Validate dataset Methods MAE(mm) MRE(%) RMSE(mm) Presim1 75.24 10 119.78 China Presim2 343.71 95 424.96 Prems 347.39 105 436.23 Presim1 74.43 4 97.27 Jiangxi Presim2 227.82 13 257.91 Prems 208.67 12 245.40

1 1 Presim- Pr e obs 1 2 MAE=Pr esim - Pr e obs , MRE = , RMSE=(Pr esim - Pr e obs ) , N k=1,⋯ , N Nk=1,⋯ , N Pr eobs N k=1,⋯ , N

The results show that the first method is much better than the second from these three error indexes for both datasets. The accuracy of the downscaling method Presim2 is worse than the result of CMIP5 based on the validate dataset in Jiangxi province. Scatter correlation plots for the observed and predicted precipitation (Figure 2) suggest that the first downscaling method estimates the annual mean precipitation quite reliably, as is shown in Figure2(a) and Figure 2(c). Many simulation points are relatively far from the straight line of y= x by using the second method. Underestimation of precipitation is evident for the points from national scale and overesti- mation of precipitation is obvious for Presim2 in Jiangxi province (see Figure2(b) and Figure2(d)). The correlation coefficient between predicted and observed values is 0.97 for Presim1 and 0.73 for Presim2 for the 10% of the total sampled points in China. The correlation coefficients are 0.75 and 0.71 for Presim1 and Presim2, respectively, in Jiangxi province.

3000 3 0 0 0 a b ) ) m m 2000 2 0 0 0 m m ( ( 2 1 m m i i s s e e r r 1000 1 0 0 0 P P

0 0 0 500 1000 1500 2000 2500 3000 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 Observed precipitation(mm) Observed precipitation(mm) 3000 3000 c d ) ) 2500 2500 m m m m ( ( 2 1 2000 2000 m m i i s s e e r r P P 1500 1500

1000 1000 1000 1500 2000 2500 3000 1000 1500 2000 2500 3000 Observed precipitation(mm) Observed precipitation(mm)

Figure 2. Observed and estimated precipitation using different methods, a) Presim1 for 10% points from China, b) Presim2 for 10% points from China, c) Presim1 for points from Jiangxi province, d) Presim2 for points from Jiangxi province.

Figure 3. The comparison of two downscaling methods, (a) original CMIP5 output, (b) the first method Presim1, (c) the second method Presim2.

Figure 3 illustrates the downscaling results. We can see that due to the large errors (as showed in Figure 3 (a)) in the original CMIP5 output, especially in southeastern of the Tibetan Plateau, the second method which used the CMIP5 output to modify the residual is worse than the first one. The distribution trends in Figure 3 (a) and Figure 3 (c) are similar, which shows that the second downscaling method didn’t modify the errors produced by CMIP5. However, Figure 3 (b), which is produced by the first downscaling method, agrees well with the real situation. The reason of this is the function of the meteorological station information. And further, we can see that original CMIP5 output is not good enough for use. The introduction of station data is necessary to modify the local details that implemented by HASM. The comparison of the two downscaling methods also re- veals that the second step in the downscaling process, that is, the residual correction, is critical important for accuracy improvement.

5. Conclusion Precipitation, as a fundamental component of the global water cycle, is a key parameter in ecology, hydrology and meteorology. Precipitation data with accurate, high spatial resolution are crucial for improving our understanding of basin-scale hydrology. In this study, we compare two statistical downscaling methods by using two dataset. One dataset scatter randomly in the whole of China and another are located in Jiangxi province. As ex-

4 Author’s name pected, the results show that GCMs cannot be used directly in climate change impact studies. In China, the sec - ond method Presim2 which establishes regression model based on the station data has a tendency to overestimate or underestimate the real values. The advantage of the first method is obvious, which fuse the mode data and station data effectively. Results also show the importance of the meteorological station data in the process of residual modification. China is such a vast area, precipitation is affected by many geographical and topographi- cal factors, which means that more accurate results can be obtained by using local regression methods with more explanatory variables, especially for short time scales. Except the variables considered in this study, further re- searches should be concentrate on more explanatory variables to gain more accurate results.

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