Advances in Meteorology

Volume 2015 (2015), Article ID 254378, 11 pages

http://dx.doi.org/10.1155/2015/254378

## On the Use of Threshold for the Ground Validation of Satellite Rain Rate

^{1}Weather Radar Center, Korea Meteorological Administration, Seoul 156-720, Republic of Korea^{2}School of Civil, Environmental and Architectural Engineering, College of Engineering, Korea University, Seoul 136-713, Republic of Korea^{3}Department of Information Statistics, College of Science and Technology, Yonsei University, Wonju,
Gangwon 222-701, Republic of Korea

Received 21 January 2015; Accepted 17 May 2015

Academic Editor: Hann-Ming H. Juang

Copyright © 2015 Jungsoo Yoon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Ground-truthing is a major problem in the satellite estimation of rain rate. This problem is that the measurement taken by the satellite sensor is fundamentally different from the one it is compared with on the ground. Additionally, since the satellite has the limited capability to measure the light rain rate exactly, the comparison should also consider the threshold value of satellite rain rate. This paper proposes a ground-truth design with threshold for the satellite rain rate. This ground-truth design is the generalization of the conventional ground-truth design which considered the only (zero, nonzero) and (nonzero, nonzero) measurement pairs. The mean-square error is used as an index of accuracy in estimating the ground measurement by satellite measurement. An application to the artificial random field shows that the proposed ground-truth design with threshold is valid as the design bias is zero. The same result is also derived in the application to the COMS (Communication, Ocean, and Meteorological Satellite) rain rate data in Korea.

#### 1. Introduction

It is a very difficult job to accurately observe the rain rate field in space. Rain gauge is the most traditional tool to measure the rainfall and is still assumed to be the most reliable one. However, rain gauge produces point measurements which may not be enough to capture the spatial characteristics of the rain rate field. Radar has advantages in that sense as it has a large spatial coverage. However, the spatial coverage of radar is still small to cover the continent or the entire earth. This is the reason why the satellite is expected to play an important role in global hydrology [1].

Satellite provides various kinds of information like the land use, vegetation, and soil moisture. Specifically, the information about the precipitation is used for the analysis of global hydrological cycle and ultimately is to be used as an input for the flood forecasting [2–5]. Many satellite programs have been underway to measure the rain rate especially in remote areas such as the Tropical Pacific [6–12]. However, the satellite also uses a sensor to indirectly measure the rain rate, whose measurement can be different from the true value. This is the reason why the validation process is required for the rain rate data through the comparison with the so-called ground-truth [13, 14].

The ground-truth problem is a complex procedure since the two sensors measure different quantities: the rain gauge measures rain rate at a point nearly continuously in time, while the satellite measures an area average of rain rate over its field of view (FOV) discretely in time. While these two estimates in the long run should agree, there could be a large random difference between the two because of the different space-time sampling configurations. It should be possible, however, by taking enough simultaneous pairs of measurements to compare them and check for bias in the satellite rain rate. Thiele [15] presents an extensive discussion of all the issues relating the ground-truth and indicates several areas of active research problem. North et al. [16] and Ha and North [17] developed a strategy that can be used to check the calibration of satellite data using the ground measurements.

The ground-truth problem is complicated by the fact that the probability distribution of real rain rate data has a significant contribution at zero rain rate (usually greater than 90%). Hence, many of the data pairs can be (no-rain, no-rain) measurements or perhaps (no-rain, rain) measurements where the second entry is the satellite data. For this reason, much more data pairs should be collected to show that there is no bias involved due to the ground-truth design. Ha and North [18] and Ha et al. [13] also proposed the ground-truth design which uses the data pairs only when the satellite measurement is positive.

Additionally, it is also known that the satellite measurement has a lot of uncertainty especially when the rain rate is very low [19–21]. This problem is related with the spectrum of the electric signal reflected from the object. When the strength of the signal is small, the SNR (signal to noise ratio) of the electric signal can decrease, which leads to larger uncertainty [22, 23]. That is, the uncertainty in the rain rate measurement can be very high when the rain rate is small [22, 23]. A simple solution to this problem is to discard the data which is lower than a certain threshold value of rain rate.

We present here a technique of validating satellite rain rate based upon the comparison with the measurements on the ground. Since the satellite rain rate is not trusty when the rain rate is very low, the ground-truth design proposed in this study uses the data pairs only when the satellite measurement exceeds a certain threshold level. The point rain gauge is used as the ground-truth measurement to validate satellite rain rate. The advantage of using the rain gauges is that they do not introduce any controversial algorithms associated with estimating the rain rate from a “ground-truth” measurement such as that derived from radar.

As an application example, this study analyzed the COMS (Communication, Ocean, and Meteorological Satellite) rain rate data in Korea. As ground-truth data, the rain rate from a total of 468 AWS (automatic weather stations) was used. The rainfall event analyzed includes the rain rate on 0800LST JUL 27 2011, whose maximum hourly rain rate recorded in Seoul, the capital city of Korea, was more than 80 mm/hr.

This paper is composed of a total of four sections, including the Introduction and Conclusions. Section 2 summarizes theoretically the comparison problem of the satellite and rain gauge rain rate with threshold. The application example to the Bernoulli random field is also provided in this section. In Section 3, a real application example with the COMS rain rate data is given.

#### 2. Theoretical Backgrounds

Ha et al. [24] presented a theoretical background on the comparison of radar and rain gauge rain rate with given thresholds. They also showed that there would be no systematic bias introduced when applying a threshold to the radar rain rate. Summarizing the theoretical background on the comparison of radar and rain gauge rain rate is as follows.

Consider a random rain rate field , defined in the plane, and along the time axis . As a typical experiment, we locate a point rain gauge at some fixed location , on the plane. The rain gauge is located inside a satellite bin, with its area . Now the rain gauge rain rate is defined asand the satellite rain rate, based on , is calculated as Obviously, the satellite rain rate of (2) corresponds to the rain gauge rain rate of (1). Thus, we have two measurements, with respect to the th rain gauge, and , where the subscripts denote the satellite and rain gauge, respectively. We form the difference between the satellite and rain gauge rain rate and call it the error for the th data pair. Here, we assume that the rain gauge rain rate is the “truth,” and only the satellite rain rate contains some error. The mean-square error, which is usually used as an index of the accuracy, when comparing the satellite rain rate to the rain gauge one, is defined by The error in the satellite rain rate for a specific rain gauge is likely to contain a large component of random error. If the members of the measurement pairs are statistically independent, we can sharpen the histogram of the difference between the satellite rain rate and the rain gauge rain rate, by adding independent data pairs.

As outlined in the introduction, the comparison with threshold uses the data pairs only when the satellite rain rate is greater than the threshold; that is, it uses data pairs when , where is the threshold. We can write the mean error for comparison that uses the threshold as follows:where denotes the conditional mean of , given that . We can also express the mean-square error as

In this study, we partition the satellite bin into (*n* ×* n*) tiles (or cells), to treat the random field effectively as a multivariate vector. The satellite rain rate can then be written aswhere is the number of subdivisions that have been chosen for the partitioning of the satellite bin and represents the area-average rain rate in an grid square, which we call a tile (or a cell). Also, the rain gauge rain rate is assumed to bewhere is the rain gauge location. For the convenience of notation, we will use and , instead of and , respectively. The satellite and rain gauge rain rates are thenWhen we compute the mean and the mean-square error, we have to consider the location of the rain gauge within the satellite bin. Since the rain gauge is located randomly within a satellite bin, we can assume to be a random number, following the uniform distribution.

Ha et al. [24] also presented an example such that the probability of rain rate in an individual tile (or cell) is and one tile is independent of the other. Since the random field here was assumed to be a white noise Bernoulli random field, the distributions of the gauge and satellite measurements areThe ground-truth design with threshold uses the data pairs only when the satellite measurements are greater than the threshold. Thus, we can derive the distribution of ground and satellite measurements with threshold using the distribution of and conditional on . Since we assumed that the random field is white noise, the probability that the satellite measurement is greater than threshold iswhere and is the largest integer less than or equal to . Note that when the random field is not white noise the probability cannot be written in this form. Finally, they derived the error distribution ,Using the derived conditional error distribution , it was shown thatThis says that the bias of the error for the ground-truth design with threshold is zero and thus the ground-truth design can be used to validate the satellite measurements.

#### 3. COMS Data Examples

##### 3.1. Data

As an application example, this study analyzed the COMS (Communication, Ocean, and Meteorological Satellite) rain rate data. The COMS is a geostationary satellite launched on June 27, 2010. The COMS is operated by the National Meteorological Satellite Center, which produces the satellite rain rate data by analyzing the satellite images with the Calibration Matrices (CMs) made from the radar information. The CM is dependent on the solar zenith angle. If the solar zenith angle is higher than the threshold angle (85°), the CM based on the images of infrared (IR-1) and water vapor (WV) is used. On the other hand, if the solar zenith angle is lower than the threshold angle, another CM based on the images of IR-1, WV, and visible (VIS) is used. Additionally, moisture correction factor, cloud growth rate correction factor, cloud-top temperature gradient correction factor, parallax correction factor, and orographic correction factor are applied to correct the rain rate estimated with the CMs.

The spatial resolution of the COMS rain rate data is 4 km × 4 km, and its temporal resolution is 15 minutes. As ground-truth data for the evaluation of the COMS rain rate data, the rain gauge data from a total of 468 AWS (automatic weather stations) were used. Figure 1 shows example images of rain rate over the northern hemisphere and over the Korean Peninsula on 0800LST JUL 27 2011. The storm event occurring at this time was a very severe one and the maximum hourly rain rate recorded in Seoul, the capital city of Korea, was more than 80 mm/hr.