Meteorology students hardly experience smooth and expeditious data analysis. When comes to results, they oftentimes plunge to nebulous insights and vague conclusions. Despite how clearly the method used, meteorology students shouldn’t take the idea of being creative in handling the data for granted. The quality of results totally depends on how creative they scramble the data and extract its insights. Hence the better result quality comes the more beneficial explanation. For the practical instance, when harnessing the time series meteorological dataset on analysis, many students trivialize the existence of another possible domain on the dataset. Many students don’t treat the time series data as a signal or wave that related to many parameters such as frequency and period. In this post, I’m going to show an uncomplicated example on how we use other possible domain of time series data -which is frequency- on analyzing meteorology phenomenon encompassing its practical step-by-step methods using python programming language.

气象专业的学生几乎不会经历流畅而Swift的数据分析。 当涉及到结果时，他们通常会陷入模糊的见解和模糊的结论。 尽管使用的方法有多清晰，但气象学学生在处理数据时不应抱有创造性的想法。 结果的质量完全取决于他们如何创造性地加扰数据并提取其见解。 因此，更好的结果质量来自更有益的解释。 在实际情况中，当利用时间序列气象数据集进行分析时，许多学生轻视了数据集上另一个可能域的存在。 许多学生不会将时间序列数据视为与许多参数(例如频率和周期)相关的信号或波。 在本文中，我将展示一个简单的示例，说明如何使用其他可能的时间序列数据域(即频率)来分析气象现象，其中包括使用python编程语言进行的实用逐步方法。

Prepare the data

准备数据

First things first, prepare the data that going to be analyzed. For example, I use 37-years daily precipitation from CHIRPS which is rainfall estimates from rain gauge and satellite observations. The data has been cropped at the specific BMKG Station in Bandung, named Cemara Weather Station. Since CHIRPS data more complete than BMKG data, I personally prefer to use CHIRPS rather than use BMKG data despite the considerable discrepancy in the data when compared.

首先，准备要分析的数据。 例如，我使用来自CHIRPS的 37年日降水量，这是根据雨量计和卫星观测得出的降雨量估算值。 数据已在万隆特定的BMKG站Cemara气象站进行了裁剪。 由于CHIRPS数据比BMKG数据更完整，因此我个人更喜欢使用CHIRPS而不是BMKG数据，尽管与之相比数据存在很大差异。

Fig 1 shows the daily precipitation (mm) from 1st January of 1981 until 31st December of 2018. We might already have known that Bandung or any other region located on Java island has two seasons (dry and rainy). The peak of rainy season in Bandung normally happens in December-January-February (DJF) and the trough of rainy season -which also called dry season- in Bandung normally happens in June-July-August. Much of research proved that seasonality weather in Bandung (and mostly western Indonesia) is affected by Asia-Australia monsoon. As we know the trend of rain seasonality, we suppose to be able to depict it as a wave or signal since it has the peak and trough. For the better overview, instead of figure the data as a panel fraught of raw points connected to each other, let’s turn it to monthly precipitation.

图1显示了从1981年1月1日到2018年12月31日的日降水量(mm)。我们可能已经知道万隆或Java岛上的任何其他地区有两个季节(干燥和多雨)。 万隆的雨季高峰通常发生在12月至1月至2月(DJF)，而万隆的雨季低谷(也称为旱季)通常发生在6月，7月至8月。 许多研究证明，万隆(主要是印度尼西亚西部)的季节性天气受亚澳季风影响。 我们知道降雨季节的趋势，因为它具有波峰和波谷，因此我们可以将其描述为波浪或信号。 为了获得更好的概览，我们不要将数据看作是相互连接的原始点的面板，而是将其转换为月降水量。

Now we have a better overview of rain seasonality in Bandung. This wavy pattern transpires one time a year and some years may have shifted of peak and trough of the rainy season. Notwithstanding, the pattern remains.

现在，我们对万隆的降雨季节有了更好的了解。 这种波浪形图案每年发生一次，并且有些年份可能已经转移了雨季的高峰和低谷。 尽管如此，模式仍然存在。

How if there were any else possibly periodically pattern occur in a year? Semiannual pattern or quarter-annually pattern? It could be and it should have been known by meteorology students as they recognize that rain pattern in Indonesia is very complex and affected by up to global-scale events and influenced by various topographic features.

一年中是否还有其他可能定期出现的模式？ 半年模式还是每半年一次？ 气象学学生应该知道，而且应该知道，因为他们认识到印度尼西亚的降雨模式非常复杂，并且受到全球范围内最大事件的影响，并受到各种地形特征的影响。

Use FFT!

使用FFT！

Fast Fourier Transform (FFT) is one of the most useful tools and widely used in signal processing. FFT has contributed to many problems solving observations in astronomy, physics, and chemistry. In meteorology, FFT has been utilized for many kinds of research and most of it is related to climate data analysis. Climate data tend to have a long period of observation which reflects scientist’s definition that climate normal as an average over a recent 30-year period.

快速傅立叶变换(FFT)是最有用的工具之一，广泛用于信号处理中。 FFT导致解决天文学，物理学和化学观测问题的许多问题。 在气象学中，FFT已用于多种研究，其中大多数与气候数据分析有关。 气候数据趋向于长期观测，这反映了科学家的定义，即最近30年的平均气候平均值。

FFT is a very complicated mathematical equation, and to be honest, I’ve never fully understood how’s the FFT equation works. To see more about FFT and how it works, check this out (A gentle introduction to the FFT). In this article, I want to introduce how to use scipy.fft library in python to decompose seasonality patterns in 37-year precipitation data and get yourself (and myself) to gradually adept with python data analysis library.

FFT是一个非常复杂的数学方程式，老实说，我从未完全理解过FFT方程的工作原理。 要了解有关FFT及其工作原理的更多信息，请检查一下( FFT的简要介绍 )。 在本文中，我想介绍如何使用python中的scipy.fft库分解37年降水数据中的季节性模式，并使自己(和我自己)逐渐适应python数据分析库。

import matplotlib

导入matplotlib

import matplotlib.pyplot as plt

导入matplotlib.pyplot作为plt

from pylab import *

从pylab导入*

from math import *

从数学导入*

import warnings

进口警告

warnings.simplefilter(‘ignore’)

warnings.simplefilter('ignore')

import numpy as np

将numpy导入为np

from numpy.fft import fftfreq

从numpy.fft导入fftfreq

from scipy.fftpack import *

从scipy.fftpack导入*

from scipy.signal import butter, filtfilt , freqz

来自scipy.signal进口黄油，filtfilt，freqz

import pandas as pd

将熊猫作为pd导入

Import all the libraries needed. Scipy is the main library use in this analysis. It contains many of FFT formulas and filtering methods. Then, read the data.

导入所有需要的库。 Scipy是此分析中主要使用的库。 它包含许多FFT公式和滤波方法。 然后，读取数据。

prec = pd.read_csv(‘prec_chirps.csv’)

prec = pd.read_csv('prec_chirps.csv')

Use pandas library to read csv to see the data as data frame like this:

使用pandas库读取csv可以将数据作为数据框查看，如下所示：

The data has 13,879 rows represents daily precipitation (mm) from 1981–2018 and has no null values. The annual seasonality in Fig. 1 can be seen by a naked eye. However, it’s not enough to present the existence of seasonality only by subjective plain sight towards a graph, thus we need more palpable images that could indicate the seasonality by exact number.

该数据有13,879行代表1981-2018年的每日降水量(mm)，没有空值。 用肉眼可以看到图1中的年度季节性。 但是，仅凭主观直视图表来呈现季节的存在是不够的，因此我们需要更多可触摸的图像，以确切的数字指示季节。

dt = 1

dt = 1

n = prec.shape[0]

n = prec.shape [0]

F = fft(prec[‘prec’])

F = fft(prec ['prec'])

w = fftfreq(n, dt)

w = fftfreq(n，dt)

t=np.linspace(1, n, n)

t = np.linspace(1，n，n)

T = n/t[0:6939]

T = n / t [0：6939]

indices = where(w > 0)

索引=其中(w> 0)

w_pos = abs(w[indices])

w_pos = abs(w [indices])

F_pos = abs(F[indices])

F_pos = abs(F [indices])

In this step, we start to use FFT to transform the precipitation data which only has time domain to frequency domain. Declare dt = 1 as long as we want to analyze the data on daily basis over a 37-year period of time. The FFT result represents by F.

在这一步中，我们开始使用FFT将仅具有时域的降水数据转换为频域。 只要我们想在37年的时间内每天分析数据，就声明dt = 1。 FFT结果用F表示。

Bear in mind that the time series precipitation data is a combination of many frequency waves which has each wave parameters and amplify one another. By transforming the data to frequency domain, we could get each set of waves with certain frequencies that build-up the data.

请记住，时间序列降水量数据是许多频率波的组合，这些频率波具有各自的波参数并相互放大。 通过将数据转换到频域，我们可以获得具有一定频率的每组波，这些波构成了数据。

Next, assign data length to n and calculate sample frequency with fftfreq function in which requires n and dt as arguments. It returns float array w contains the frequency bin centers in cycles per unit of the sample spacing (with zero at the start). Don’t forget to set synthetic data variable which represents the time array with an increasing value from 1 until n (data length). Then, set a new variable that portrays the number of periodicity types of the signal whereby the length is half of the original data. After that, select only indices for elements that correspond to positive frequencies. To know the details about why we do this step, check this thread: Why is FFT “mirrored”?

接下来，将数据长度分配给n并使用fftfreq函数计算采样频率，其中需要n和dt作为参数。 它返回的浮点数组w包含频率单元中心，以每个采样间隔单位的周期为周期(开始时为零)。 不要忘记设置合成数据变量，该变量代表时间数组，其值从1到n(数据长度)递增。 然后，设置一个新变量，该变量描述信号的周期性类型的数量，其中长度是原始数据的一半。 之后，仅选择与正频率相对应的元素的索引。 要了解有关为什么执行此步骤的详细信息，请检查以下线程： 为什么FFT是“镜像”的？

Now, we’re all set to figure the desirable of time-domain transformation to the frequency domain.

现在，我们都准备好将时域转换为频域的理想方法。

fig1 = plt.figure()

图1 = plt.figure()

ax = fig1.add_axes([0, 0, 2, 0.8])

斧= fig1.add_axes([0，0，2，0.8])

axF = fig1.add_axes([0, 1.2, 2, 0.8])

axF = fig1.add_axes([0，1.2，2，0.8])

axF.plot(w_pos, abs(F_pos))

axF.plot(w_pos，abs(F_pos))

axF.set_xlabel(‘Frequency’, fontsize = 13)

axF.set_xlabel('Frequency'，fontsize = 13)

axF.set_ylabel(‘magnitude’, fontsize = 13)

axF.set_ylabel('magnitude'，fontsize = 13)

axF.set_title(‘Periodogram (FFT Result)’, fontsize = 15)

axF.set_title('周期图(FFT结果)'，fontsize = 15)

axF.tick_params(labelsize = 13)

axF.tick_params(labelsize = 13)

ax.plot(T, abs(F_pos))

ax.plot(T，abs(F_pos))

ax.set_xlabel(‘Period’, fontsize = 13)

ax.set_xlabel('Period'，fontsize = 13)

ax.set_ylabel(‘magnitude’, fontsize = 13)

ax.set_ylabel('magnitude'，fontsize = 13)

ax.set_title(‘Periodogram (FFT Result)’, fontsize = 15)

ax.set_title('周期图(FFT结果)'，fontsize = 15)

ax.tick_params(labelsize = 13)

ax.tick_params(labelsize = 13)

The graph called periodogram. The difference between the two graphs above is on the x-axis. The upper graph shows periodogram with frequency as an x-axis, on the contrary, the lower graph uses 1/frequency (period) as x-axis. I found that the lower graph is way more intuitive and comprehensible since the period’s unit is the same as the data time unit which is a day. The y-axis is the amplitude of each periodicity/frequency that build-up the data. From the lower graph, it can be seen that from the 37-years length of data, the highest contributions are ranging between lower period sub-signal for exact < 1000 days of a period. Let’s point out that range.

该图称为周期图。 上面两个图表之间的差异在x轴上。 上方的图显示频率为x轴的周期图，相反，下方的图使用1 /频率(周期)为x轴。 我发现较低的图形更加直观和易于理解，因为时间段的单位与一天的数据时间单位相同。 y轴是建立数据的每个周期性/频率的幅度。 从下面的图表中可以看出，从37年的数据长度来看，最大的贡献介于精确到<1000天的较低周期子信号之间。 让我们指出这个范围。

By limiting the x-axis range, we get the clear-cut of the periodicity ranges which have a significant amplitude in forming the original data. Without being examined, 365-days periodicity has the highest amplitude as I mentioned earlier. It clearly represents the most common and well-known of Bandung rain seasonality (annual seasonality). The second highest amplitude is on 183-days (~6-month, semi-annual seasonality) and the third is on 122-days (~4-month, quarter-annual seasonality). It turns out that Bandung rain seasonality is not only transpired annually, but it also has semi-annual and quarter-annual patterns, nevertheless, the amplitude is not quite high which means that the patterns are less frequent to exist over the time scope of the data.

通过限制x轴范围，我们可以清楚地看到周期性范围，该范围在形成原始数据时具有明显的幅度。 如前所述，未经检查，365天的周期具有最高的振幅。 显然，它代表了万隆雨季最常见和最著名的一年(季节性)。 第二高的振幅是在183天(约6个月，每半年一次的季节性)，而第三高的振幅是在122天(约4个月，每半年一次的季节性)。 事实证明，万隆的降雨季节不仅每年发生一次，而且还具有半年和四分之一的规律，但幅度并不很高，这意味着在整个时间范围内这些规律的存在频率较低。数据。

Meteorologically, these patterns could happen inflicted by various events such as local disturbances until global variabilities like El Nino-La Nina or Madden-Julian Oscillation (MJO) effects. We should need more researches to be able to answer the cause of these available patterns of Bandung rainfall seasonality. Python programming language with its user-friendly scientific package has been bringing us to advance the data analysis regarding many sectors. This simple use case in meteorology maybe not as complex as other use cases, but it worth knowing and worth sharing. After using FFT and knowing the hidden patterns of the data, there are so many analysis tools which also practical to meteorological science use cases, like filtering (low-pass, band-pass, high-pass filtering) and many more. Hope this article is pertinent to your study field and could help you to get more profound data analysis.

在气象上，这些模式可能是由各种事件(例如局部扰动)造成的，直到像El Nino-La Nina或Madden-Julian振荡(MJO)效应这样的全球变率为止。 我们应该进行更多的研究，才能回答万隆降雨季节性变化的这些可用模式。 Python编程语言及其用户友好的科学软件包已使我们推进了许多领域的数据分析。 气象学中的这个简单用例可能没有其他用例那么复杂，但是值得了解和分享。 使用FFT并了解数据的隐藏模式后，有许多分析工具对气象科学用例也很实用，例如滤波(低通，带通，高通滤波)等等。 希望本文与您的研究领域相关，并且可以帮助您获得更深入的数据分析。