Investigation of Daily Rainfall Distribution Using the NRC Method (Case Study: Tabriz, Maragheh, Urmia and Mahabad)

Study of various aspects of daily rainfalls is so crucial from the view of scientific management of water resources in every region. Iran is located in subtropical high-pressure belt, which had low annual rainfall. The precipitation regime is very irregular both in time and space. The East and West Azarbaijan provinces are known as the important areas of agriculture, especially cereal production in Iran. Therefore, study of temporal and spatial distribution of daily rainfalls is very important in this region. The purpose of this study is to extract the best model for normalized rainfall curves (NRC) in the four selected stations namely, Tabriz, Maragheh, Urmia and Mahabad.
In this study, daily rainfalls of four stations namely, Tabriz, Maragheh, Urmia and Mahabad were used to fit the normalized rainfall curves (NRC). For this purpose, the two custom hydrologic models i.e. and were employed for NRCs. In order to find the values of (cumulative percentage of daily rainfalls) firstly the amount of daily rainfalls observations were arranged in ascending Order. Then, cumulative percent of rainfall calculated during the time period. The NRC curves of each station, plotted by drawing the versus for a total statistical period, separately. This was done for a given month (eg, January) data across the whole period and whole day's rainfall during the consecutive months of the years of the study period. In the latter case, the daily rainfalls of the first month of the first year of the study period were written consecutively in a distinct column of Excel spreadsheets. Then, daily rainfalls of the second year were written similarly, following the first years data. Daily rainfalls of the third, fourth and so on were written consecutively in the same mentioned column of Excel spreadsheets. Similarly, another column attributed to the number of rainy days in the studied period. Then, the values of non-zero daily rainfalls (arranged in ascending order) accumulated consecutively, and the resulted value were divided to the total number of observed rainfalls in the period (R). Similarly cumulative rainy days were divided to the total days (N). Moreover, the other fifteen models (including the power, exponential ...), were tested for the stations observations separately. Among the mentioned models, the most suitable one is selected according to RMSE and criteria.
Results showed that the maximum amount of daily rainfall experienced in Mahabad station in the rainiest month of the year or April (equivalent to 68 mm per day). The minimum value of daily rainfall belonged to the August (equivalent to 6 mm per day). The shape of NRCs created in this study for period in each of the four stations, showed that these curves were concave in almost all of the cases. This implies that a small amount of rainfall fell in a long period. In addition, the results showed that nearly in all of the stations the model of had the lowest value of RMSE and the largest value of . Therefore, this model selected as the most suitable one for NRCs of the stations. Although, the Exponential Association (3) model (in Tabriz) in April and the 4th degree Polynomial model (in Mahabad) in August selected as the most suitable model for them. Furthermore, the difference of statistics for the two models (at both of the time series) obtained as less than 0.0001. In the rainiest month and driest month of a year, the range of RMSE varied between 0.2559 mm in April (Maragheh) and 0.6709 mm in April (Tabriz). Moreover, the values varied between 0.9992 in August (Maragheh) and 0.9999 in April (Maragheh). In general, it can be concluded that the amount of precipitation receives in half of the rainy days is less than fifteen percent of the total rainfall depth. In this study, the values of of the most appropriate model for Tabriz, Urmia, Maragheh, Mahabad obtained as equal to 0.9996, 0.9997, 0.9996 and 0.9994, respectively.
Among the 17 candidate models, the model number 2 showed the highest , and the lowest RMSE. Therefore, the model was selected as the most appropriate model for drawing NRCs. Also, the mentioned model, were selected as the most appropriate model for all the months (in the four stations). The results showed that the NRCs were concave and in most cases, a small amount of total rainfall fell during the large number of days. In addition, in the two stations namely, Tabriz and Urmia the amount of rainfall receives in the 25, 50, 75 and 90 percent of rainy days were about two, 10, 30 and 60 percent of the total rainfall depth, respectively