Digital Proceeding of IREEC – 2015 Saber Moazami, M.Reza Kavianpour (Editors)
Prague, Czech Republic, June 4-6, 2015
Copula-Based Analysis of Satellite Rainfall Estimation Error Saber Moazami1, M.Reza Kavianpour2, and Saeed Golian3 1
Assistant Professor, Department of Civil Engineering, College of Engineering, Islamshahr Branch, Islamic Azad University, Islamshahr, Tehran, IRAN (Email:
[email protected]) 2
Associate Professor, School of Civil Engineering, K.N.Toosi University of Technology, Tehran, Iran (Email:
[email protected]) 3
Assistant Professor, Civil Engineering Department, Shahrood Univerity of Technology, Shahrood, Iran (Email:
[email protected])
ABSTRACT The objective of this paper is to error analysis of two widely-used 0.25 0.25 satellite rainfall estimate (SRE) algorithms, named PERSIANN and TRMM (TMPA-3B42) using copula. In this study, the daily products of SREs from 2002 to 2006 have been compared with ground rain gauges data in a part of Iran. Because of uneven distribution of ground stations in the study area that lead to an unreliable analysis of satellite rainfall estimation error, it seems important to develop a model that determine the spatial error dependence between rain gauges. Then in the present work a type of copula functions, named Gaussian copula has been used to evaluate the error distribution of SREs. The procedure started with the calculation of daily biases of SREs with considering of ground stations as a reference data. A 100 year long time series of daily satellite rainfall error then has been generated by the Gaussian copula. This long-term continuous error simulation resulted in characterizing the spatial dependence of error between grid cells in the study area. It was also resulted in estimating the biases of SREs in different probability level of precipitation in various parts of the study region.
Keywords: Copula, Error, PERSIANN, Satellite rainfall estimates, TMPA-3B42.
1.INTRODUCTION High resolution satellite rainfall estimates (SREs) are a useful source of datasets for hydrological applications and water resources planning. In this study, the main purpose is to evaluate the accuracy of SREs in Iran. It is noteworthy that in this country, the availability of ground measuring stations is very limited because of the sparse density of hydrometeorological networks which make it challenging for accurate flood predictions and other 1
hydrological applications. However, SREs are tending to larger errors in comparison with ground based radar and rain-gauge precipitation, due to the indirect nature of satellite estimates. Then we need to calibrate the SREs with conventional gauges and data to provide improved information. For this purpose, a copula-based method was implemented to simulate and adjust the bias of two satellite products, PERSIANN (Hsu et al. 1997) and TRMM (Huffman et al. 2010). 2. BACKGROUND The evaluation of the accuracy of SREs have been carried out at different spatial and temporal resolution in several researches in the last years (AghaKouchak et al. 2012; Behrangi et al. 2011; Su et al. 2008; Tian et al. 2007; Hong et al. 2007; Hirpa and Gebremicheal, 2010; Li et al. 2009; Bitew and Gebremicheal, 2011). Furthermore, some researches in regard to applications of copula functions in diverse fields of hydrology and remotely sensed rainfall simulations have been done. (Aghakouchak et al. 2010; Evin and Favre, 2008; Zhang and Singh, 2007; Renard and Lang, 2007; Grimaldi and Serinaldi, 2006). 3. METHODOLOGY 3.1. Study area The study area of this research to evaluate SREs includes the entire country of Iran with a total area of 1,648,195 km2 (Figure.1 (a)). In addition, Khuzestan Province in the southwest of Iran with a total area of 64,236 km2 (Figure.1 (b)) was selected to adjust of obtained biases from SREs evaluation. (a)
(b)
Figure 1. Study area, (a) Distribution of rain gauges (blue circles), synoptic stations (red triangles) and satellite pixels over Iran, (b) Khuzestan Province
3.2. Data resources Rain gauge data are provided by Iran Water Resources Management Co. (IWRM) and synoptic station data are provided by Iran Meteorological Organization (IMO). We used daily precipitation data of 940 rain gauges and 240 synoptic stations from 2002 to 2006. These ground station data were considered as a reference data. The satellite rainfall products that were used in this study were based on PERSIANN and TRMM algorithms. PERSIANN and TRMM products are available from to globally and estimate precipitation at a spatial resolution of Latitude/longitude. We used the daily temporal resolution of these products because the rain gauge data were based on daily resolution. 2
3.3. Verification of satellite-based daily precipitation Verification of SREs over Iran was conducted by comparing the rainfall estimates with the gauge observed rainfall data for 58 selected events from 2002 to 2006. The factor of Multiplicative bias (Mbias) (Equation 1) was used to evaluate the performance of SREs. It provides an estimate of whether the SREs tend to underestimate by value of less than one or overestimate by value of greater than one. (1) Where PS and PO is the rainfall value of satellite data and gauge observed at each event, respectively. N is the number of pixels which both satellite and rain gauge have recorded a non-zero rainfall amount at each event. 3.4. Copula-based bias generation Copulas are joint cumulative distribution functions that describe dependencies among variables independent of their marginal (Joe, 1997 and Nelsen, 2006)). To complete the definition, let indicate a set of n random variables and a realization of it. Then copula is a function that links the multivariate distribution univariate marginals
to its
. Sklar(1959) demonstrated that : =
(2)
For two random variables x and y with continuous probability distributions of F(x) and G(y), Sklar(1959) defined that: (3) Where
is the joint probability distribution and
is its corresponding copula,
and
. 4. RESULTS AND DISCUSSION Figure 2 (a) and (b) represents the spatial pattern of the event-based mean Mbias factor, respectively for the PERSIANN and TRMM in the selected pixels of study area. As shown in this figure, a Mbias ratio greater than one indicates overestimation by the SREs, less than one indicates underestimation by the SREs, and a Mbias ratio of one indicates no bias in the SREs. The country-averaged Mbias ratio of Iran is 0.89 for PERSIANN and 1.65 for TRMM. So, PERSIANN tends to underestimate rainfall, while TMPA tends to overestimate it, and because the result of PERSIANN is closer to one, it would be more accurate than TRMM over the study area.
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(a)
(b)
Figure 2. Mean Mbias of SREs at each pixel over Iran : (a) PERSIANN, (b) TRMM
In addition, to adjust the bias of SREs, random bias samples were generated using copula method. Bias is the difference of rainfall value between the gauge observed and the satellite estimated . The bias adjustment of SREs was applied over twenty satellite pixels ( ) in Khuzestan Province. Figure 3 represents the comparison between original SREs and three bias-adjusted (simulated) rainfall probability levels of PERSIANN and TRMM for two daily events over Khuzestan. As shown in this figure the 50% mean level of the bias-adjusted rainfall is more close to the gauge observed rainfall than the original rainfall estimates (unadjusted) that indicates the implemented method of Gaussian copula is capable to improve the SREs properly.
(a)
(b)
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(c)
(d)
Figure 3. Comparison of original SREs, rain gauge observations , and bias-adjusted SREs at three probability levels of 10%, 50%, and 90% for PERSIANN : (a) and (b), and TRMM : (c) and (d). (vertical and horizontal axes represent the rainfall value (mm/day) and the number of pixel, respectively).
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