بررسی خصوصیات زمانی- مکانی بارش با استفاده از تبدیل موجک گسسته حداکثر همپوشانی (modwt) و ابزار خوشه‌بندی مکانی

بارندگی یکی از عناصر مهم آب و هوایی بوده و از عوامل تاثیرگذار در چرخه‌ی هیدرولوژیکی محسوب می‌شود. تغییرات زمانیمکانی بارش در یک حوضه، می‌تواند اثرات متعددی بر مهندسی، مدیریت و برنامه‌ریزی منابع آب آن حوضه داشته باشد. در تحقیق کنونی جهت بررسی خصوصیات بارش ماهانه 30 ایستگاه واقع در جنوب شرقی کشور ایالات‌متحده طی سال‌های 2018-1968، از دو روش کلاسیک و پیشنهادی استفاده گردید. در روش پیشنهادی، از روش پیش‌پردازش سری زمانی شامل تبدیل موجک گسسته ماکزیمم همپوشانی  (modwt)به همراه خوشه‌بندی kmeansاستفاده شد. ابتدا سری زمانی بارش ماهانه ایستگاه‌ها با استفاده از روش modwt و موجک مادر db به چندین زیر سری زمانی تجزیه‌ شد. سپس، انرژی زیر سری‌ها محاسبه و به‌عنوان ورودی روش های k-means و rbf مورد استفاده قرار گرفت. تعداد خوشه های بهینه برای ایستگاه‌ها در هر دو روش کلاسیک و پیشنهادی پنج خوشه به دست آمد. جهت استفاده از داده ها به‌عنوان ورودی روش rbf ابتدا، همبستگی داده‌ها توسط نمودارهای واریوگرام و کوواریانس بررسی شد. سپس، روش spline with tension در مدل rbf انتخاب و نقشه‌های پهنه‌بندی رسم گردید. بر اساس نتایج خوشه‌بندی و مطابق با تغییرات در طول و عرض جغرافیایی ایستگاه ها، مشخص گردید که با افزایش انرژی خوشه‌ها، مقدار بارش در ایستگاه‌های آن خوشه کاهش می یابد و بالعکس. مقادیر ضریب سیلوئت خوشه بندی در روش کلاسیک 0.3 و در روش پیشنهادی 0.8 به دست آمد که این امر، نشان‌دهنده خوشه بندی بهتر ایستگاه های مورد مطالعه در روش پیشنهادی است.

Investigation of Temporal-Spatial Characteristics of Precipitation Using Discrete Maximal Overlap Wavelet Transform (MODWT) and Spatial Clustering Tools

Precipitation is one of the important climatic elements and is one of the factors affecting the hydrological cycle. Temporalspatial variations of precipitation in a watershed can have numerous effects on the engineering, management and planning of water resources. Many researchers have been studied precipitation variations. Most hydrological time series are nonstationary, trendy, or with seasonal fluctuations. Wavelet analysis is one the commonly applied approaches by researchers. It has been utilized as a common tool to break down and excavate complex, periodic, and irregular hydrological and geophysical time series, especially in recent years. On the other hand, clustering techniques can be used to identify structure in an unlabeled precipitation data set by objectively organizing data into homogeneous groups where the withingroupobject dissimilarity is minimized and the betweengroupobject dissimilarity is maximized. Clustering analysis is similar to the homogeneity test. Considering the dynamic characteristics and nonuniform distribution of precipitation data and due to the need for identifying of homogeneous precipitation regions in water resources management, a temporalspatial model is proposed to investigate the characteristics of precipitation. The time series of the precipitation were decomposed using MODWT mothod and the energy of subseries was culculated. MODWT is a mathematical technique which transforms a signal into multilevel wavelet and scaling coefficients. Maximal overlap discrete wavelet transform (MODWT) is similar to the discrete wavelet transform (DWT) in that lowpass and highpass filters are applied to the input signal at each level. However, the MODWT does not decimate the coefficients and the number of wavelet and scaling coefficients is same as the number of sample observation at every level of the transform. In other words, MODWT coefficients consider the result of a simple changing in the pyramid algorithm used in computing DWT coefficients through not down sampling the output at each scale and inserting zeros among coefficients in the scaling and wavelet filters. Clustering is the process of partitioning or grouping a given set of patterns into disjoint clusters. This is done such that patterns in the same cluster are alike and patterns belonging to two different clusters are different. kmeans clustering is a method of vector quantization, originally from signal processing, that is popular for cluster analysis in data mining. kmeans clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. RBF methods have their origins in techniques for performing the exact interpolation of a set of data points in a multidimensional space. RBF mappings provide an interpolating function which passes exactly through every data point. In the present study, the classical and proposed methods were used to investigate the monthly rainfall characteristics of 30 stations in the southeastern of United States during 1968 2018. In the proposed method, the time series preprocessing method including MODWT discrete wavelet transform and Kmeans clustering were used. At first the monthly precipitation time series of the stations were districted into several subseries using MODWT method and db mother wavelet. Then, the energy of subseries was calculated and used as input for Kmeans and RBF methods. The optimum number of clusters for the stations in both classical and proposed methods was five clusters. In order to use the data as the input of the RBF method, the correlation of the data was evaluated by variogram and covariance graphs. Then Spline with Tension method was selected in RBF model and zoning maps were drawn. In order to evaluate the temporalspatial characteristics of monthly rainfall of 30 selected stations, two classical and proposed methods were used. At first the monthly precipitation time series of the stations were districted into several subseries using MODWT method and db mother wavelet. Then, the energy of subseries was calculated and used as input for Kmeans and RBF methods. The optimum number of clusters for the stations in both classical and proposed methods was five clusters. In order to use the data as the input of the RBF method, the correlation of the data was evaluated by variagram and covariance graphs. Based on the results of clustering and in accordance with the latitude and longitude variations of the stations, it was found that with increasing the energy of the clusters, the amount of precipitation in the stations decreased and vice versa. Silhouette coefficient of clustering in classical method was 0.3 and in proposed method was 0.8, which indicates better clustering of studied stations in the proposed method.