Calibration of seasonal transfer equation (Z – R) by data of Doppler weather radar, rainfall gauging station and genetic algorithm method in the Abolabbas watershed (in southwest of Iran)

The observed radar re ﬂ ectivity (Z) converts to rainfall intensity (R) by a transfer function. In the ﬁ rst stage, for calibration of collected data (with time step 15 minutes) by weather radar and determination of the best relation between Z and R, it applied a genetic algorithm (GA) to minimize the amount of root mean square error (RMSE). Although Z ¼ 166R 2 (the transfer function in the Khuzestan province of Iran) is an appropriate equation, the GA method distinguished that Z ¼ 110R 1.8 (from February to May) and Z ¼ 126R 2 (for other months) are the optimum transfer functions for the Abolabbas watershed in Iran. The mean of RMSE of optimum transfer equations is 0.59 mm/hr in the calibration stage and 0.85 mm/hr in the veri ﬁ cation stage. In the second stage, the Hydrologic Modeling System (HEC-HMS model) used four types of precipitation data (extracted rainfall data from radar and the optimum transfer equations, Z ¼ 166R 2 , Z ¼ 200R 1.6 and extracted rainfall data from rainfall gauging stations). The calibrated rainfall data by the optimum transfer equations can produce ﬂ ood hydrographs in which their accuracy is similar to the accuracy of generated ﬂ ood hydrographs by collected rainfall data of rainfall gauging stations. The mean of RMSE is 0.65 cubic metres per second and the mean or R 2 is 0.89 for optimum transfer equations. optimization method for determination of the transfer function Z – R and considering seasonal characteristics of precipitation that can distinguish two transfer functions Z – R. (cid:129) Using a rainfall – runoff model for determination of accuracy of the derived functions Z – R.


INTRODUCTION
The use of technologies and tools as weather radars and satellite images for measurement of meteorological phenomena (temperature, precipitation, etc.) is a conventional method in developed countries. But in developing countries, the use of these tools is new approach. Therefore meteorologists and hydrologist must calibrate extracted data from these tools. In the Middle East countries such as the Khuzestan province of Iran, although the main source of climatic information is extracted meteorological skilled data from synoptic weather stations, the quantity and quality of these data may not be appropriate for several reasons. Occurrence of the Iran-Iraq war (1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988) River Basin of China and converted them to rainfall intensity for a heavy rainfall event in July 2007. They calibrated data collected by radar using measured data from rainfall gauges and observed that error in estimated rainfall intensity by radar networks is less than 45%. Josephine et al. () used hourly data from Doppler weather radars and rainfall gauges to estimate runoff using the the Hydrologic Modeling System (HEC-HMS model). Their case study was Chennai basin, Tamil Nadu, India. They observed that difference between simulated volumes of two hydrographs is negligible, while difference between simulated peak discharges and time to peaks of two hydrographs is high (the sources of rainfall data of two simulated hydrographs are data from Doppler weather radar and rainfall gauges). Maity et al. () applied a copula-based approach for determination of uncertainty of the transfer function Z-R (radar reflectivity (Z) and rainfall intensity (R)) in India and observed that this approach is a suitable tool for this purpose. Keblouti et al. () used data from weather radar for simulation of runoff in Seybouse, Annaba watershed in north-eastern Algeria. Simulated runoff using data from weather radar was more accurate than simulated runoff of rainfall data from rainfall gauges. Lagrange et al. () applied the wavelet-based scattering transform for classification of collected data by weather radar. These data concern the Nantes region of western France over 23 rainy days in 2009 and 2012. This method classified radar images well and its accuracy was 93.5%. Moreau et al. Accuracy of calibrated rainfall data by this transfer equation will be compared with accuracy of collected rainfall data from rainfall gauging stations. Therefore the HEC-HMS rainfall-runoff model produces flood hydrographs using these two types of rainfall data and compares these hydro-

Verification of the extracted transfer function Z-R for the
Abolabbas watershed by HEC-HMS rainfall-runoff model. For this purpose, simulated runoff according to generated rainfall data using this equation will be compared with simulated runoff according to rainfall data from rainfall gauges.
The new aspects of this research are: 1. Extraction of the transfer function Z-R for a special watershed. This subject can increase precision of data of weather radar for simulation of rainfall-runoff.
Because of occurrence of dust storms and similarity of size of dust particles and rain drops, this approach is necessary for this region.
2. The use of time intervals less than 1 hr for rainfall hyeto-  The sender model is 1,500 TXS and the digital signal processor model is Aspen DRX. The software used for the weather radar are Selex ES-Gematronik and Rainbow ® 5. Vertical rotational angle is between À2 to 90 . Figure 2 shows the Am Altamir S-Band weather radar and its position relative to the Abolabbas watershed.

Research methodology
Research methodology of this research includes the following steps: 1 -Selection of recorded rainfall gauging station for determination of the best transfer equation between the   (Table 1).    Performance criteria

-Extraction
The used performance criteria are: Mean error (ME): where Q c is calculated flow discharge (CMS), Q c is observed flow discharge (CMS) and n is number of observations.
Mean absolute error (MAE): Root mean square error (RMSE): Mean bias error (MBE): Normalized root mean square error (NRMSE): Correlation coefficient (R 2 ): RMSE, NRMSE, MAE and ME values should be close to zero and MBE and R 2 should be close to one. Also it used the recession method for base flow separation and the Muskingum method for flood routing in the river. Figure 4 shows the curve number (CN) map of the watershed.

RESULTS
Calibrated parameters of the model for five flood hydrographs are given (Table 3).
In the verification stage, the value of parameters is the geometric mean of calibrated values of parameters using HEC-HMS.
The performance criteria values for different calibrated and verified flood hydrographs are given (Table 4).
The HEC-HMS rainfall-runoff model considers the peak discharge of flood hydrographs and volume of stream flow for calibration and verification of different flood hydrographs.
where Q pobs is observed peak discharge of flood hydrograph and Q pcal is calculated peak discharge of flood hydrograph.  The characteristics of applied GA in this research are: where R obs is observed rainfall intensity at the rainfall gauging station and R cal is calculated rainfall intensity using the optimum transfer function. Corrected Proof while at other months the type of precipitation is frontal rainfall (light to moderate rainfalls). Type of rainfall can affect the observed radar reflectivity (Z). It should be noted that using an optimum transfer function alone increases RMSE and reduces R 2 . The RMSE and R 2 for Z ¼ 110R 1.8 alone are 0.92 mm/hr and 0.9 respectively and the RMSE and R 2 for Z ¼ 126R 2 alone are 0.65 mm/hr and 0.93 respectively. Figure           accuracy of the derived optimum transfer equations (Z ¼ 110R 1.8 and Z ¼ 126R 2 ) is more than the accuracy of the transfer equation (Z ¼ 166R 2 ). Because the derived optimum transfer equations concern different periods of the year and they were derived for two types of precipitations, heavy to violent rainfall and light to moderate rainfall.
Performance criteria values for two flood hydrographs are given (Table 7). Table 7 show that the optimum transfer equations have the most fitness with observed data in comparison to other transfer equations. Therefore for each watershed, suitable transfer equations must be derived.

DATA AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.