# Efficient and accurate estimation of water surface velocity in STIV

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## Abstract

In shallow flow conditions, turbulence effects appear on a water surface as a form of irregularity of surface shape composed of a large number of fluctuating ripples. The intensity of such a fluctuation increases with the Froude number and also with the Reynolds number as can be observed in flooding river flow. In such a flow condition, surface irregularities are viewed as surface features or textures moving with the flow. Although there has been a discussion in terms of the traceability of surface features, the advection speed of surface features agrees well with the surface velocity from a practical point of view. Based on the assumption about the traceability of surface features, image-based techniques have been developed in the past decades. The space–time image velocimetry (STIV) is one of those techniques developed by Fujita et al. (Int J River Basin Man 5(2):105–114, 2007), with success of measuring river surface velocity distributions without seeding the flow. However, there is still some room for improvement in determining accurate surface velocity from a space–time image (STI) used in STIV. For that purpose, a novel technique was developed that utilizes the two dimensional auto-correlation function of the image intensity in an STI together with quality indices of STI. The performance of the new technique was verified using synthetic images as well as its application to the measurement of snowmelt flood.

## Keywords

Surface velocity measurement Image-based technique STIV LSPIV## 1 Introduction

Disasters caused by floods occur everywhere in the world in small to large river basins, with their intensity increasing probably due to the global climate change in recent years [33]. In order to prepare for such disasters by establishing a proper risk management scheme and river improvement plan, it is crucial to systematically acquire accurate hydrological information such as rainfall intensity distributions, water level and discharge. Among these hydrological parameters, the number of flow measurement points and the flow data are much less than the other parameters, because accurate discharge measurement is difficult to conduct especially in flood conditions. On the other hand, it is indispensable from the viewpoint of water resources management to accurately measure the discharge even at low flow rates. Regarding typical measurement at high-flow rates, estimation of discharge is conducted from in situ measurements of flow velocity by using impellor-type current meters, acoustic Doppler velocimeters, or acoustic Doppler current profilers (ADCP) [22] coupled with measurements of bathymetry. However, in Japan, a float method is officially used in major rivers in the last several decades [21], because of the difficulty of using intrusive measurement instrument at high-velocity flows with various flotsams such as driftwood or floating objects. The floats are made of cardboard pipe in which certain amount of sand is contained to control its specific gravity close to unity when it floats. According to the Japanese regulation, floats with different lengths are used depending on the water depth; e.g. two-meter float is used when the water depth is greater than 2.6 m. The longest float is 4 m and used for a depth greater than 5.2 m. In the float method, the time that a float passes through a specified length, usually about one hundred meter, is measured by a stop watch by a pair of field workers. The transverse spacing of the float measurement is about ten to twenty meters, suggesting that a discharge of a river with one hundred meter has to be measured only by using four floats in case of emergency. Such a rapid measurement has to be conducted because a hydrograph tends to show a sharp peak with a duration of a few hours in Japan. Therefore, the available measurement time would become very short to obtain the flow rate at nearly the same water level, leading to a possibility that a significant error might occur in the data. In addition, this method becomes difficult to carry out in case of a huge flood that could overflow the levee because of the danger of measurement works itself.

The most possible solution to the problem is to use image-based techniques such as the large-scale particle image velocimetry (LSPIV) [2, 3, 6, 8, 9, 10, 12, 23, 24, 26, 27, 28, 29] or the space–time image velocimetry (STIV) [1, 13, 14, 19, 30]. These techniques can measure surface velocity distributions by analyzing surface images captured from a river bank. The fundamental assumption behind the techniques is that visible texture on the water surface acts as a passive tracer relative to the surface flow. The surface texture is basically a superposition of turbulence-generated surface ripples moving in all directions. The above assumption has been verified in various field measurements at least when the wind effect is negligible [5, 32, 34, 35]. To compare LSPIV with STIV, the former measures an instantaneous velocity vector using a pair of images with a specified time separation while the latter measures an averaged velocity in space and time at a specified spacing usually set in the streamwise direction by using all images at once. With respect to discharge measurement, STIV is superior to LSPIV, especially when the depression angle of image shooting is small and the pixel resolution farther from the camera location becomes low [35].

However, even in STIV, measurement errors might occur in the cases where the quality of surface textures are not appropriate for the image analysis due to random noises, white caps by wave breaking, standing surface waves, shadow of background projected on the water surface close to shoreline, etc. In STIV, a streamwise array of pixels is sampled over time to create a temporal image sequence or time stack, which we call space–time image (STI) in this paper. Since sloped features in the space–time image represent the advection velocity of surface texture, measurement becomes difficult when the STI includes textures that do not directly related to the streamwise flow due to the above-mentioned factors. Therefore, for establishing a reliable measurement system, deteriorated STI has to be detected by setting a threshold with respect to the quality of STI. In this paper, we proposed a new algorithm using autocorrelation function for space–time images and its performance is evaluated through the comparison with the other techniques. The new technique is termed the quality evaluation of STI by using two dimensional autocorrelation function (QESTA).

## 2 Outline of the conventional STIV

### 2.1 Generation of space–time image

### 2.2 The standardization (STD) filter

*I*(

*x,t*) is the original pixel intensity distribution of a space–time image,

*I*

^{S}(

*x,t*) is the filtered image,

*μ*

_{t}(

*x*) is the mean value of pixel intensity for a vertical array given by

*σ*

_{t}(

*x*) is the standard deviation for the pixel array calculated by

The effect of the STD filter is provided in Fig. 2. It is obvious that the texture in each STI became much clearer by normalizing the image by the standard deviation for each vertical pixel array. For example, the shade appeared in STI30 or STI130 h disappeared completely in STI30 s and furthermore the imbedded linear texture have emerged after applying the STD filter.

*ϕ*is larger in the center of the section while they become smaller closer to each bank, indicating the flow is gradually accelerated in the middle of the section and decelerated near the flow boundaries. The basic idea behind STIV is that once such a linear texture is obtained in STI, a space-and-time averaged streamwise velocity can be calculated merely by measuring the slope of the texture.

### 2.3 Conventional method of STIV

In the conventional STIV developed by Fujita et al. [13], the STI is partitioned into rectangular subregions where local texture gradient is calculated by the optical gradient tensor method [13, 25]. The mean gradient value is obtained by first generating a histogram of gradients and then taking the weighted average of them by using the coherency of the local image as a weighting factor [1, 13]. Alternatively, two dimensional Fast Fourier transformation (FFT) using a band pass filter can be used to improve the quality of STI by picking up only the pattern related to the flow [11, 15]. The conventional STIV has been successfully applied to several flood flow measurements [1, 18], but it is difficult to evaluate the quality of STI based on the optical gradient tensor method. Other than the above technique [4, 7] developed a similar approach (optical current meter, OCM) for alongshore currents in the nearshore environment, but the information about the quality of STI was not provided in their research [5, 32].

## 3 A new algorithm of STIV

### 3.1 Detection of pattern gradient using 2D auto-correlation function

*f*(

*x,y*) is the image intensity distribution in STI and (

*τ*

_{x}

*τ*

_{y}) are shift parameters. To calculate the autocorrelation function efficiently, the Wiener–Khinchin theorem is utilized that states the inverse Fourier transform of the power spectral density function gives the autocorrelation function, i.e.

*F*

^{−1}stands for the inverse Fourier transform. With this theorem, the autocorrelation function of an STI can be numerically calculated efficiently by using the Fast Fourier Transform algorithm. As an example, the distribution of the autocorrelation function

*R*(

*τ*

_{x}

*τ*

_{y}) of the STI shown in Fig. 4a is provided in Fig. 4b. The distribution is normalized such that

*R*(0,0) takes a value of one at the centre of the autocorrelation image, i.e. \(\hat{R}(\tau_{x} ,\tau_{y} ) = R(\tau_{x} ,\tau_{y} )/R\left( {0,0} \right)\). It is apparent that the region of higher correlation shows an inclined pattern corresponding to the actual texture gradient.

*R*(

*τ*

_{x}

*τ*

_{y}) within a circle indicated in Fig. 4b was transformed to the logarithmic polar coordinates (

*ρ*,

*θ*) shown in Fig. 4c by taking the origin at the centre of Fig. 4b. The transformation equation is

*M*is the coefficient of intensification and

*M*= 15 is used in this example. The purpose of using the log-polar coordinates is to emphasize the information near the origin which is important for accurately obtaining the texture gradient. The darker region in Fig. 4c corresponds to a larger correlation region near the origin. Finally, in order to find the peak value of the gradient, the distribution in Fig. 4c is averaged in the

*ρ*direction to obtain the directional average distribution (DAD) μ(

*θ*) by,

*θ*) from π/2, i.e.

*S*

_{x}is the unit physical length scale per pixel in the lateral direction and

*S*

_{t}is the unit time scale per pixel in the downward vertical direction of STI.

### 3.2 Quality evaluation parameters of STI

As mentioned in the introduction, the accuracy of the STIV depends on the quality of STI and it is necessary to pick up only reliable STI for establishing a real time measurement system. In this research, two parameters for evaluating the STI quality are proposed; i.e. the Poisson ratio (ν)-type index NTI, and the shear deformation (γ)-type index GTI.

#### 3.2.1 Poisson type index NTI

*μ*(

*θ*), which is written as

#### 3.2.2 The relation between the texture gradient and the error in measurement

*ϕ*indicating the flow is obtained by Eq. (11), the relationship between

*ϕ*and the measurement error can be derived as follows. The relation between velocity and the texture gradient shown in Eq. (12) can be simply expressed as the following relation with

*k*being a constant coefficient;

*u*due to the gradient measurement error

*Δϕ*can be expressed by the following relation,

*p*can be given as

It is clear from the functional feature of Eq. (16), *p* takes the minimum value at 45 degrees for the same error of Δ*ϕ*. On the other hand, the error increases significantly for textures with smaller or larger angles.

#### 3.2.3 The shear effect index GTI

*ϕ*in Eq. (15) with the phase difference \(\Delta \hat{\phi }\) indicated in Eq. (17), which can be calculated by

The method presented above including the measurement of texture gradient as well as the use of indices for evaluating the STI quality is hereafter termed the Quality evaluation of STI by using two-dimensional autocorrelation function (QESTA).

## 4 Evaluation of QESTA

For evaluating the accuracy and performance of QESTA, synthetic space time images with various texture gradients are examined.

### 4.1 Synthetic data test

### 4.2 Measurement accuracy of QESTA

## 5 Application of QESTA to flood flow measurement

### 5.1 Outline of the measurement site

The performance of the new STIV algorithm, QESTA, was examined by applying it to the measurement of snowmelt flood of the Uono River, which is a major tributary of the Shinano River that flows into the Japan Sea. The measurements were carried out downstream and upstream of the Negoya Bridge, located at Horinouchi in Uonuma City of Niigata Prefecture Japan on April 24, 2014. The measurements were conducted by shooting video images by using a high-definition camera from the left bank. The width of water at the upstream section was about 160 m at the time of measurement. During the image shooting, measurements by a remote-controlled and boat-mounted ADCP was concurrently conducted at the upstream section taking a rout in a zig-zag manner to cover a larger river reach. As the upstream measurement section by STIV, already indicated in Fig. 1, agrees with one of the trajectories of ADCP, comparisons were made in terms of the transverse velocity distribution. STIV analysis was conducted by setting search lines with a length of 23.0 m and a spacing of 5.46 m as already mentioned. In addition, LSPIV analysis was conducted at the same section to compare the relative accuracy.

### 5.2 Comparison of surface velocity distributions

^{3}/s, GTM 232.25 m

^{3}/s, QESTA with STD filter 234.65 m

^{3}/s, and LSPIV 246.79 m

^{3}/s. The relative error to ADCP is 3.6% in GTM, 4.7% in QESTA, and 10.1% in LSPIV. In LSPIV, velocity components in the direction of search lines is used for discharge calculation. Regarding the NTI value, Fig. 10 shows the application of the STD filter raises its value about 0.5, indicating the improvement of texture in STI.

### 5.3 Efficiency of analysis

The advantage of STIV over LSPIV is its efficiency of analysis. In LSPIV, sequential ortho-rectified images with a very large image size have to be prepared, therefore it would require a large storage volume and time for the analysis. On the other hand, STIV basically generates a STI with a small image size for the search line and does not require large storage volume as in LSPIV. In the present case, the genuine CPU time to calculate one velocity data was 0.94 s in STIV and 2.06 s in LSPIV when we use a normal Windows PC. In addition, the storage size required in LSPIV was 3.59 GB for saving 358 rectified bitmap images with a size of 2296 by 1806 pixels, while STIV used only 21.0 MB in the present analysis.

## 6 Conclusions

A new technique for measuring river surface velocity distributions by using video images shoot obliquely from a riverbank was proposed, together with indices for evaluating the quality of space time images. As a measurement method for river flow discharge, only the float method has been officially allowed in the last several decades in Japan. However, due to the difficulty of float measurements in extreme flow conditions in flood disasters in recent years, methods other than the float method have come to be allowed officially from 2017 in Japan. Therefore, image-based techniques such as LSPIV and STIV have been paid attention and among them STIV is recognized as a promising technique for extracting reasonable results, because measurements can be executed safely and economically by utilizing existing river monitoring cameras. The advantage of STIV over LSPIV is that STIV can yield reliable results even when the image shooting is carried out under deteriorated light conditions. The measurement system using STIV is commercialized as a software KU-STIV (be-system.co.jp/navi_soft/soft_kustiv/kustiv.htm) in 2015, and since then STIV has been used successfully in many first-class rivers in Japan. Although a tentative real-time measurement system with STIV is already established [17, 20], space time images occasionally become difficult to handle in dark–light condition. Therefore, it is necessary to pick up only reliable STIs and discard unreliable ones for discharge estimation. From the viewpoint of practical measurement, the quality evaluation by GTI or NTI can be used as indices, although the threshold levels of the two indices have not been determined in the present research. Hence, further examinations under much more deteriorated conditions have to be executed. Finally, thanks to the development of unmanned aerial vehicles (UAVs) in recent years, river flow images have come to be utilized for measurements of much longer river reach by using aerial STIV technique using an efficient image stabilizing technique [16], which will be a promising technique to investigate river flows difficult to access from the ground.

## Notes

### Acknowledgements

This research was supported by the River Foundation’s River Fund and Grant-in-Aid for Scientific Research. I express my gratitude here.

## References

- 1.Aberle J, Rennie CD, Admiraal DM, Muste M (2017) Experimental hydraulics, methods, instrumentation, data processing and management, Vol: II instrumentation and measurement techniques. CRC Press, Boca RatonCrossRefGoogle Scholar
- 2.Aya S, Fujita I, Yagyu M (1995) Field observation of flood in a river by video image analysis. Proc. Hydraul. Eng 39:447–452CrossRefGoogle Scholar
- 3.Bradley AA, Kruger A, Meselhe E, Muste M (2002) Flow measurement in streams using video imagery. Water Resour Res 38(12):1315. https://doi.org/10.1029/2002WR001317 CrossRefGoogle Scholar
- 4.Chickadel C, Holman RA, Freilich MH (2003) An optical technique for the measurement of longshore currents. J Geophys Res 108(C11):3364. https://doi.org/10.1029/2003JC001774 CrossRefGoogle Scholar
- 5.Chickadel C, Talke SA, Horner-Devine A, Jessup AT (2011) Infrared-based measurements of velocity, turbulent kinetic energy. IEEE Geosci RemoteSens Lett 8:849–853. https://doi.org/10.1109/LGRS.2011.2125942 CrossRefGoogle Scholar
- 6.Costa JE, Spicer KR, Cheng RT, Haeni FP, Melcher NB, Thurman EM, Plant WJ, Keller WC (2000) Measuring stream discharge by non-contact methods: a proof-of-concept experiment. Geophys Res Lett 27(4):553–556. https://doi.org/10.1029/1999GL006087 CrossRefGoogle Scholar
- 7.Drew PJ, Blinder P, Cauwenberghs G, Shih AY, Kleinfeld D (2010) Rapid determination of particle velocity from space-time images using the Radon transform. J Comput Neurosci 29:5–11. https://doi.org/10.1007/s10827-009-0159-1 CrossRefGoogle Scholar
- 8.Dramais G, Le Coz J, Camenen B, Hauet A (2011) Advantages of mobile LSPIV method for measuring flood discharges and improving stage-discharge curves. J Hydro Env Res 5(4):301–312CrossRefGoogle Scholar
- 9.Fujita I, Komura S (1994) Application of video image analysis for measurements of river surface flows. Annual J Hydraul Eng JSCE 38:733–738
**(in Japanese)**CrossRefGoogle Scholar - 10.Fujita I, Muste M, Kruger A (1998) Large-scale particle image velocimetry for flow analysis in hydraulic engineering applications. J Hydraul Res 36(3):397–414CrossRefGoogle Scholar
- 11.Fujita I, Ando T, Tsutsumi S, Hara H (2009) Efficient space-time image analysis of river surface pattern using two dimensional fast Fourier transformation. In: Proceedings of the 33rd IAHR Congress, pp. 2272–2279Google Scholar
- 12.Fujita I, Aya S (2000) Refinement of LSPIV technique for monitoring river surface flows. Build Partnersh. https://doi.org/10.1061/40517(2000)312 CrossRefGoogle Scholar
- 13.Fujita I, Watanabe H, Tsubaki R (2007) Development of a non-intrusive and efficient flow monitoring technique: the space time image velocimetry (STIV). Int J River Basin Man 5(2):105–114CrossRefGoogle Scholar
- 14.Fujita I, Kosaka Y, Honda M, Yorozuya A (2012) Tracking of river surface features by space time imaging. In: Proceedings of the 15th international symposium on flow visualization (ISFV15) ISFV15-045:S23Google Scholar
- 15.Fujita I, Asami K, Kumano G (2014) Evaluation of 2D river flow simulation with the aid of image-based field velocity measurement techniques. Proc River Flow 2014:1969–1977Google Scholar
- 16.Fujita I, Notoya Y, Shimono M (2015) Development of UAV-based river surface velocity measurement by STIV based on high-accurate image stabilization techniques. In: E-proceedings of the 36th IAHR world congress: 80824.pdfGoogle Scholar
- 17.Fujita I, Kobayashi K, Logahm FY, Teyeoblim F, Alfa B, Tateguchi S, Kankam-Yeboah K, Appiah G, Asante-Sasu CK, Kawasaki R, Ishikawa H (2015) Accuracy of KU-STIV for discharge measurement inGhana, Africa. J JSCE Ser. B1 (Hydraul Eng) 73(4):I_499-I_504Google Scholar
- 18.Fujita I (2017) Discharge measurements of snowmelt flood by space-time image velocimetry during the night using far-infrared camera. Water 9(4):269. https://doi.org/10.3390/w9040269 CrossRefGoogle Scholar
- 19.Fujita I, Kitada M, Shimono M, Kitsuda T, Yorozuya A, Motonaga Y (2017) Spatial measurements of snowmelt flood by image analysis with multiple-angle images and radio-controlled ADCP. J JSCE 5(1):305–312CrossRefGoogle Scholar
- 20.Fujita I, Deguchi T, Doi K, Ogino D, Notoya Y, Tateguchi S (2017) Development of KU-STIV: software to measure surface velocity distribution and discharge from river surface images. In: Proceedings of the 37th IAHR world congress, pp 5284–5292Google Scholar
- 21.Fukami K, Yamaguchi T, Imamura H, Tashiro Y (2008) Current status of river discharge observation using non-contact current meter for operational use in Japan. In: World environmental and water resources congress, pp 1–10Google Scholar
- 22.Gordon L (1989) Acoustic measurement of river discharge. J Hydraul Eng 115:925–936CrossRefGoogle Scholar
- 23.Hauet A, Creutin JD, Belleudy P (2008) Sensitivity study of large-scale particle image velocimetry measurement of river discharge using numerical simulations. J Hydrol 349:178–190. https://doi.org/10.1016/j.jhydrol.2007.10.062 CrossRefGoogle Scholar
- 24.Holland KT, Holman RA, Lippmann TC, Stanley J, Plant N (1997) Practical use of video imagery in nearshore oceanographic field studies. IEEE J Oceanic Eng 22(1):81–92CrossRefGoogle Scholar
- 25.Jahne B (1993) Spatio-temporal image processing: theory and scientific applications. Springer, New YorkCrossRefGoogle Scholar
- 26.Jodeau M, Hauet A, Paquier A, Le Coz J, Dramais G (2008) Application and evaluation of LS-PIV technique forthe monitoring of river surface velocities in high flow conditions. Flow Meas Instrum 19:117–127CrossRefGoogle Scholar
- 27.Le Coz J, Hauet A, Pierrefeu G, Dramais G, Camenen B (2010) Performance of image-based velocimetry (LSPIV) applied to flash-flood discharge measurements in Mediterranean rivers. J Hydrol 394(1–2):42–52CrossRefGoogle Scholar
- 28.Lee MC, Leu JM, Chan HC, Huang WC (2010) The measurement of discharge using a commercial digital video camera in irrigation canals. Flow Meas Instrum 21:150–154CrossRefGoogle Scholar
- 29.Muste M, Fujita I, Hauet A (2008) Large-scale particle image velocimetry for measurements in riverine environments. Water Resour Res 44:W00D19. https://doi.org/10.1029/2008wr006950 CrossRefGoogle Scholar
- 30.Muste M, Hauet A, Fujita I, Legout C, Ho HC (2014) Capabilities of large-scale particle image velocimetry to characterize shallow free-surface flows. Adv Water Res 70:160–171CrossRefGoogle Scholar
- 31.Perlin K (2002) Improving noise. ACM Trans Gr (TOG) 21:681–682Google Scholar
- 32.Puleo JA, McKenna TE, Holland KT, Calantoni J (2012) Quantifying riverine surface currents from time sequences of thermal infrared imagery. Water Resour Res 48:W01527. https://doi.org/10.1029/2011WR010770 CrossRefGoogle Scholar
- 33.Schiermeier Q (2011) Increased flood risk linked to global warming: likelihood of extreme rainfall may have been doubled by rising greenhouse-gas levels. Nature 470(7334):316CrossRefGoogle Scholar
- 34.Sun X, Shiono K, Chandler JH, Rameshwaran P, Sellin RHJ, Fujita I (2010) Discharge estimation in a small irregular river suing LSPIV. Water Manag 163:247–254. https://doi.org/10.1680/wama.2010.163.5.247 CrossRefGoogle Scholar
- 35.Tsubaki R, Fujita I, Tsutsumi S (2011) Measurement of the flood discharge of a small-sized river using an existing digital video recording system. J Hydro Environ Res 5(4):313–321CrossRefGoogle Scholar

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