# # # #的问题我想找出\ ce}{二氧化碳浓度趋势美元计算的数据提供的地球系统研究实验室莫纳罗亚山天文台。数据包含每月测量,季节性修正趋势,并插入数据填补缺口。趋势和插值数据应该从原始的可计算的平均水平。我试图复制计算趋势和插值的结果,但我保持稍微偏离值。我试过两个公式计算趋势,我叫*民用*和* formula2 *下面也再现了数据准确,虽然formula2似乎符合很好。![在这里输入图像描述][1]# # # #的数据数据[(esrl.noaa.gov)][2]作为一个文本文件结构如下:#(-99.99缺失的数据;1 #每日意味着月没有数据)# # #十进制平均插值趋势#天(季节corr) 1958 1958 1958.208 315.71 315.71 314.62 1 1958.292 317.45 317.45 315.29 1 1958 1958 1958.375 317.50 317.50 314.71 1 1958.458 -99.99 317.10 314.85 1。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。在这里* *平均的平均每月测定\ ce}{二氧化碳浓度ppm美元单位,* #天*是每月的有效天数的测量是否可用。另外两个列,* * *插值和趋势*是稍微复杂一些。文件描述的方法计算值如下。>“插值”列包含从前面列平均值>,插值数据在哪里失踪。 Interpolated values are > computed in two steps. **First**, we compute for each month the average seasonal > cycle in a 7-year window around each monthly value. In this way the seasonal > cycle is allowed to change slowly over time. We then determine the "trend" > value for each month by removing the seasonal cycle; this result is shown in > the "trend" column. Trend values are linearly interpolated for missing months. > The interpolated monthly mean is then the sum of the average seasonal cycle > value and the trend value for the missing month. ## The formulas ## In order to avoid dealing with boundary effects I compare the results past the first 3.5 years of record, so that centered 7-year windows can be correctly defined. That is starting from September 1961. Let $x_t, t=1..N$ be the monthly average values. I need to first compute "*the average seasonal cycle in a 7-year window around each monthly value*". And then substract it from the data to obtain the trend. As I understand the average seasonal cycle is the difference between the seasonal filter and some seasonal average. To compute the 7-year seasonal filter for each $t \geq 3*12 + 6$ I compute $s_t = \frac{1}{7}\Sigma_{j=-3}^{j=3}x_{t+12j}$. Now for a seasonal average I tried two options. 1. The 7-year seasonal filter average $f_t=\frac{1}{12}\Sigma_{j=0}^{j=11}s_{t+j}$ 2. The 7-year average $a_t=\frac{1}{84}\Sigma_{j=-42}^{j=41}x_{t+j}$ Thereby *formula1* is $x_t-(s_t-f_t)$ and *formula2* is $x_t-(s_t-a_t)$. ## Conclusion ## It seems to me that I misunderstand what is meant by "*the average seasonal cycle in a 7-year window around each monthly value*". Neither $(s_t-f_t)$, nor $(s_t-a_t)$ defined above fit. What is the correct formula? I have put the data into a read-only ([Google sheet][3]) for a quick check. [1]: http://i.stack.imgur.com/YVNu9.png [2]: http://www.esrl.noaa.gov/gmd/ccgg/trends/ [3]: https://docs.google.com/spreadsheets/d/1D1ndBLGDfF5t65754HiXE_bVtgNwR1GDvwOFOCJ7J2A/edit?usp=sharing