Rainfall intensity from a tipping bucket

Question

In the field of hydrology, it is common to work with rainfall data from a tipping bucket. It registers every time the bucket is filled with, for instance, 0.2 mm or 0.5 mm of water.

I would like to import this kind of data to R, but could not find a smooth way to do it. I got very good help from answers to the question Creating regular 15-minute time-series from irregular time-series, but I still miss one part of how we usually process the data: smoothing during low-intensity rainfall.

This is a small part of my data from a tipping bucket in Malmö, Sweden. 0.2 is registered for every 0.2 mm of rainfall:

Rainfall Depth[millimeter]:Instantaneous    Undefined[undefined]:Instantaneous
Time    M05_Bulltofta_vippning  Flag
2014-08-31 04:09:22 0.2 0
2014-08-31 04:12:14 0.2 0
2014-08-31 04:17:49 0.2 0
2014-08-31 04:20:00 0.2 0
2014-08-31 04:22:10 0.2 0
2014-08-31 04:23:31 0.2 0
2014-08-31 04:24:49 0.2 0
2014-08-31 04:25:49 0.2 0
2014-08-31 04:28:14 0.2 0
2014-08-31 04:36:22 0.2 0
2014-08-31 04:41:06 0.2 0
2014-08-31 04:42:58 0.2 0
2014-08-31 04:43:33 0.2 0
2014-08-31 04:45:03 0.2 0
2014-08-31 04:47:47 0.2 0
2014-08-31 04:49:49 0.2 0
2014-08-31 04:51:35 0.2 0
2014-08-31 04:52:58 0.2 0
2014-08-31 04:54:32 0.2 0
2014-08-31 04:55:54 0.2 0
2014-08-31 04:58:36 0.2 0
2014-08-31 05:02:17 0.2 0
2014-08-31 05:06:21 0.2 0
2014-08-31 05:09:56 0.2 0
2014-08-31 05:12:57 0.2 0
2014-08-31 05:14:38 0.2 0
2014-08-31 05:16:13 0.2 0
2014-08-31 05:17:42 0.2 0
2014-08-31 05:19:05 0.2 0
2014-08-31 05:20:38 0.2 0
2014-08-31 05:22:44 0.2 0
2014-08-31 05:24:11 0.2 0
2014-08-31 05:25:41 0.2 0
2014-08-31 05:26:48 0.2 0
2014-08-31 05:27:24 0.2 0
2014-08-31 05:27:59 0.2 0
2014-08-31 05:28:59 0.2 0
2014-08-31 05:29:40 0.2 0
2014-08-31 05:30:09 0.2 0
2014-08-31 05:30:33 0.2 0
2014-08-31 05:31:03 0.2 0
2014-08-31 05:31:38 0.2 0
2014-08-31 05:32:30 0.2 0
2014-08-31 05:33:46 0.2 0
2014-08-31 05:35:10 0.2 0
2014-08-31 05:36:25 0.2 0
2014-08-31 05:38:20 0.2 0
2014-08-31 05:40:38 0.2 0
2014-08-31 05:44:23 0.2 0
2014-08-31 05:44:53 0.2 0
2014-08-31 05:45:19 0.2 0
2014-08-31 05:45:55 0.2 0
2014-08-31 05:46:50 0.2 0
2014-08-31 05:47:30 0.2 0
2014-08-31 05:48:09 0.2 0
2014-08-31 05:48:26 0.2 0
2014-08-31 05:48:38 0.2 0
2014-08-31 05:48:47 0.2 0
2014-08-31 05:48:59 0.2 0
2014-08-31 05:49:15 0.2 0
2014-08-31 05:49:34 0.2 0
2014-08-31 05:50:00 0.2 0
2014-08-31 05:50:31 0.2 0
2014-08-31 05:50:51 0.2 0
2014-08-31 05:51:20 0.2 0
2014-08-31 05:52:00 0.2 0
2014-08-31 05:52:39 0.2 0
2014-08-31 05:53:01 0.2 0
2014-08-31 05:53:29 0.2 0
2014-08-31 05:53:54 0.2 0
2014-08-31 05:54:21 0.2 0
2014-08-31 05:54:43 0.2 0
2014-08-31 05:55:04 0.2 0
2014-08-31 05:55:28 0.2 0
2014-08-31 05:55:49 0.2 0
2014-08-31 05:56:05 0.2 0
2014-08-31 05:56:27 0.2 0
2014-08-31 05:56:52 0.2 0
2014-08-31 05:57:24 0.2 0
2014-08-31 05:57:56 0.2 0
2014-08-31 05:58:34 0.2 0
2014-08-31 05:59:08 0.2 0
2014-08-31 05:59:43 0.2 0
2014-08-31 06:00:11 0.2 0
2014-08-31 06:00:36 0.2 0
2014-08-31 06:00:54 0.2 0
2014-08-31 06:01:14 0.2 0
2014-08-31 06:01:28 0.2 0
2014-08-31 06:01:47 0.2 0
2014-08-31 06:02:03 0.2 0
2014-08-31 06:02:22 0.2 0
2014-08-31 06:02:43 0.2 0
2014-08-31 06:03:09 0.2 0
2014-08-31 06:03:40 0.2 0
2014-08-31 06:04:32 0.2 0
2014-08-31 06:05:26 0.2 0
2014-08-31 06:06:18 0.2 0
2014-08-31 06:07:13 0.2 0
2014-08-31 06:08:23 0.2 0
2014-08-31 06:09:24 0.2 0
2014-08-31 06:10:13 0.2 0
2014-08-31 06:10:46 0.2 0
2014-08-31 06:11:24 0.2 0
2014-08-31 06:11:47 0.2 0
2014-08-31 06:12:08 0.2 0
2014-08-31 06:12:23 0.2 0
2014-08-31 06:12:40 0.2 0
2014-08-31 06:12:55 0.2 0
2014-08-31 06:13:14 0.2 0
2014-08-31 06:13:30 0.2 0
2014-08-31 06:13:49 0.2 0
2014-08-31 06:14:08 0.2 0
2014-08-31 06:14:31 0.2 0
2014-08-31 06:14:51 0.2 0
2014-08-31 06:15:12 0.2 0
2014-08-31 06:15:33 0.2 0
2014-08-31 06:15:50 0.2 0
2014-08-31 06:16:07 0.2 0
2014-08-31 06:16:27 0.2 0
2014-08-31 06:16:43 0.2 0
2014-08-31 06:17:01 0.2 0
2014-08-31 06:17:19 0.2 0
2014-08-31 06:17:36 0.2 0
2014-08-31 06:17:51 0.2 0
2014-08-31 06:18:08 0.2 0
2014-08-31 06:18:25 0.2 0
2014-08-31 06:18:46 0.2 0
2014-08-31 06:19:05 0.2 0
2014-08-31 06:19:25 0.2 0
2014-08-31 06:19:42 0.2 0
2014-08-31 06:20:00 0.2 0
2014-08-31 06:20:12 0.2 0
2014-08-31 06:20:24 0.2 0
2014-08-31 06:20:36 0.2 0
2014-08-31 06:20:56 0.2 0
2014-08-31 06:21:14 0.2 0
2014-08-31 06:21:27 0.2 0
2014-08-31 06:21:37 0.2 0
2014-08-31 06:21:48 0.2 0
2014-08-31 06:22:06 0.2 0
2014-08-31 06:22:16 0.2 0
2014-08-31 06:22:29 0.2 0
2014-08-31 06:22:47 0.2 0
2014-08-31 06:23:09 0.2 0
2014-08-31 06:23:30 0.2 0
2014-08-31 06:23:57 0.2 0
2014-08-31 06:24:21 0.2 0
2014-08-31 06:24:39 0.2 0
2014-08-31 06:24:51 0.2 0
2014-08-31 06:25:03 0.2 0
2014-08-31 06:25:16 0.2 0
2014-08-31 06:25:29 0.2 0
2014-08-31 06:25:39 0.2 0
2014-08-31 06:25:49 0.2 0
2014-08-31 06:25:59 0.2 0
2014-08-31 06:26:13 0.2 0
2014-08-31 06:26:29 0.2 0
2014-08-31 06:26:50 0.2 0
2014-08-31 06:27:13 0.2 0
2014-08-31 06:27:49 0.2 0
2014-08-31 06:28:12 0.2 0
2014-08-31 06:28:42 0.2 0
2014-08-31 06:29:11 0.2 0
2014-08-31 06:29:44 0.2 0
2014-08-31 06:30:14 0.2 0
2014-08-31 06:30:35 0.2 0
2014-08-31 06:30:49 0.2 0
2014-08-31 06:31:06 0.2 0
2014-08-31 06:31:25 0.2 0
2014-08-31 06:31:56 0.2 0
2014-08-31 06:32:45 0.2 0
2014-08-31 06:34:09 0.2 0
2014-08-31 06:34:53 0.2 0
2014-08-31 06:35:27 0.2 0
2014-08-31 06:36:05 0.2 0
2014-08-31 06:36:25 0.2 0
2014-08-31 06:36:39 0.2 0
2014-08-31 06:36:56 0.2 0
2014-08-31 06:37:11 0.2 0
2014-08-31 06:37:24 0.2 0
2014-08-31 06:37:38 0.2 0
2014-08-31 06:37:50 0.2 0
2014-08-31 06:38:00 0.2 0
2014-08-31 06:38:12 0.2 0
2014-08-31 06:38:22 0.2 0
2014-08-31 06:38:32 0.2 0
2014-08-31 06:38:42 0.2 0
2014-08-31 06:38:52 0.2 0
2014-08-31 06:39:02 0.2 0
2014-08-31 06:39:16 0.2 0
2014-08-31 06:39:29 0.2 0
2014-08-31 06:39:42 0.2 0
2014-08-31 06:39:58 0.2 0
2014-08-31 06:40:20 0.2 0
2014-08-31 06:40:48 0.2 0
2014-08-31 06:41:23 0.2 0
2014-08-31 06:42:03 0.2 0
2014-08-31 06:42:42 0.2 0
2014-08-31 06:43:21 0.2 0
2014-08-31 06:43:46 0.2 0
2014-08-31 06:44:14 0.2 0
2014-08-31 06:44:41 0.2 0
2014-08-31 06:45:11 0.2 0
2014-08-31 06:46:01 0.2 0
2014-08-31 06:46:50 0.2 0
2014-08-31 06:47:32 0.2 0
2014-08-31 06:47:56 0.2 0
2014-08-31 06:48:21 0.2 0
2014-08-31 06:48:36 0.2 0
2014-08-31 06:48:51 0.2 0
2014-08-31 06:49:02 0.2 0
2014-08-31 06:49:17 0.2 0
2014-08-31 06:49:37 0.2 0
2014-08-31 06:50:09 0.2 0
2014-08-31 06:50:41 0.2 0
2014-08-31 06:51:24 0.2 0
2014-08-31 06:52:10 0.2 0
2014-08-31 06:52:55 0.2 0
2014-08-31 06:53:34 0.2 0
2014-08-31 06:54:10 0.2 0
2014-08-31 06:54:43 0.2 0
2014-08-31 06:55:34 0.2 0
2014-08-31 06:57:01 0.2 0
2014-08-31 06:58:27 0.2 0
2014-08-31 06:59:10 0.2 0
2014-08-31 07:00:17 0.2 0
2014-08-31 07:01:25 0.2 0
2014-08-31 07:02:19 0.2 0
2014-08-31 07:03:06 0.2 0
2014-08-31 07:04:03 0.2 0
2014-08-31 07:04:48 0.2 0
2014-08-31 07:05:31 0.2 0
2014-08-31 07:06:14 0.2 0
2014-08-31 07:06:58 0.2 0
2014-08-31 07:07:33 0.2 0
2014-08-31 07:08:19 0.2 0
2014-08-31 07:08:58 0.2 0
2014-08-31 07:09:50 0.2 0
2014-08-31 07:10:38 0.2 0
2014-08-31 07:11:34 0.2 0
2014-08-31 07:12:12 0.2 0
2014-08-31 07:13:09 0.2 0
2014-08-31 07:14:16 0.2 0
2014-08-31 07:15:07 0.2 0
2014-08-31 07:15:45 0.2 0
2014-08-31 07:16:21 0.2 0
2014-08-31 07:16:53 0.2 0
2014-08-31 07:17:30 0.2 0
2014-08-31 07:18:33 0.2 0
2014-08-31 07:19:24 0.2 0
2014-08-31 07:20:07 0.2 0
2014-08-31 07:21:06 0.2 0
2014-08-31 07:21:53 0.2 0
2014-08-31 07:22:46 0.2 0
2014-08-31 07:23:45 0.2 0
2014-08-31 07:24:59 0.2 0
2014-08-31 07:25:50 0.2 0
2014-08-31 07:26:41 0.2 0
2014-08-31 07:27:18 0.2 0
2014-08-31 07:27:59 0.2 0
2014-08-31 07:28:29 0.2 0
2014-08-31 07:29:01 0.2 0
2014-08-31 07:29:54 0.2 0
2014-08-31 07:30:51 0.2 0
2014-08-31 07:31:53 0.2 0
2014-08-31 07:32:25 0.2 0
2014-08-31 07:32:53 0.2 0
2014-08-31 07:33:21 0.2 0
2014-08-31 07:33:47 0.2 0
2014-08-31 07:34:08 0.2 0
2014-08-31 07:34:22 0.2 0
2014-08-31 07:34:42 0.2 0
2014-08-31 07:35:07 0.2 0
2014-08-31 07:35:30 0.2 0
2014-08-31 07:35:52 0.2 0
2014-08-31 07:36:18 0.2 0
2014-08-31 07:36:45 0.2 0
2014-08-31 07:37:13 0.2 0
2014-08-31 07:37:32 0.2 0
2014-08-31 07:37:49 0.2 0
2014-08-31 07:38:07 0.2 0
2014-08-31 07:38:28 0.2 0
2014-08-31 07:38:49 0.2 0
2014-08-31 07:39:04 0.2 0
2014-08-31 07:39:14 0.2 0
2014-08-31 07:39:25 0.2 0
2014-08-31 07:39:35 0.2 0
2014-08-31 07:39:45 0.2 0
2014-08-31 07:40:42 0.2 0
2014-08-31 07:40:57 0.2 0
2014-08-31 07:41:36 0.2 0
2014-08-31 07:42:23 0.2 0
2014-08-31 07:42:42 0.2 0
2014-08-31 07:43:16 0.2 0
2014-08-31 07:44:21 0.2 0
2014-08-31 07:45:19 0.2 0
2014-08-31 07:46:02 0.2 0
2014-08-31 07:47:12 0.2 0
2014-08-31 07:47:39 0.2 0
2014-08-31 07:47:58 0.2 0
2014-08-31 07:48:14 0.2 0
2014-08-31 07:48:25 0.2 0
2014-08-31 07:48:36 0.2 0
2014-08-31 07:48:48 0.2 0
2014-08-31 07:49:04 0.2 0
2014-08-31 07:49:18 0.2 0
2014-08-31 07:49:31 0.2 0
2014-08-31 07:49:52 0.2 0
2014-08-31 07:50:28 0.2 0
2014-08-31 07:51:22 0.2 0
2014-08-31 07:52:20 0.2 0
2014-08-31 07:53:13 0.2 0
2014-08-31 07:54:09 0.2 0
2014-08-31 07:55:22 0.2 0
2014-08-31 07:56:25 0.2 0
2014-08-31 07:57:17 0.2 0
2014-08-31 07:57:46 0.2 0
2014-08-31 07:58:06 0.2 0
2014-08-31 07:58:26 0.2 0
2014-08-31 07:58:43 0.2 0
2014-08-31 07:59:02 0.2 0
2014-08-31 07:59:20 0.2 0
2014-08-31 07:59:32 0.2 0
2014-08-31 07:59:48 0.2 0
2014-08-31 08:00:06 0.2 0
2014-08-31 08:00:29 0.2 0
2014-08-31 08:00:50 0.2 0
2014-08-31 08:01:14 0.2 0
2014-08-31 08:01:36 0.2 0
2014-08-31 08:02:01 0.2 0
2014-08-31 08:02:24 0.2 0
2014-08-31 08:02:41 0.2 0
2014-08-31 08:02:53 0.2 0
2014-08-31 08:03:08 0.2 0
2014-08-31 08:03:23 0.2 0
2014-08-31 08:03:37 0.2 0
2014-08-31 08:03:51 0.2 0
2014-08-31 08:04:05 0.2 0
2014-08-31 08:04:22 0.2 0
2014-08-31 08:04:40 0.2 0
2014-08-31 08:05:00 0.2 0
2014-08-31 08:05:26 0.2 0
2014-08-31 08:05:54 0.2 0
2014-08-31 08:06:23 0.2 0
2014-08-31 08:06:49 0.2 0
2014-08-31 08:07:20 0.2 0
2014-08-31 08:07:53 0.2 0
2014-08-31 08:08:32 0.2 0
2014-08-31 08:09:00 0.2 0
2014-08-31 08:09:25 0.2 0
2014-08-31 08:09:46 0.2 0
2014-08-31 08:10:12 0.2 0
2014-08-31 08:10:48 0.2 0
2014-08-31 08:11:27 0.2 0
2014-08-31 08:12:09 0.2 0
2014-08-31 08:13:06 0.2 0
2014-08-31 08:14:07 0.2 0
2014-08-31 08:14:33 0.2 0
2014-08-31 08:15:01 0.2 0
2014-08-31 08:15:23 0.2 0
2014-08-31 08:15:55 0.2 0
2014-08-31 08:16:22 0.2 0
2014-08-31 08:16:49 0.2 0
2014-08-31 08:17:17 0.2 0
2014-08-31 08:17:33 0.2 0
2014-08-31 08:17:48 0.2 0
2014-08-31 08:17:59 0.2 0
2014-08-31 08:18:12 0.2 0
2014-08-31 08:18:23 0.2 0
2014-08-31 08:18:35 0.2 0
2014-08-31 08:18:46 0.2 0
2014-08-31 08:18:59 0.2 0
2014-08-31 08:19:12 0.2 0
2014-08-31 08:19:26 0.2 0
2014-08-31 08:19:43 0.2 0
2014-08-31 08:20:07 0.2 0
2014-08-31 08:20:30 0.2 0
2014-08-31 08:20:50 0.2 0
2014-08-31 08:21:09 0.2 0
2014-08-31 08:21:30 0.2 0
2014-08-31 08:21:49 0.2 0
2014-08-31 08:22:08 0.2 0
2014-08-31 08:22:23 0.2 0
2014-08-31 08:22:38 0.2 0
2014-08-31 08:22:54 0.2 0
2014-08-31 08:23:16 0.2 0
2014-08-31 08:23:36 0.2 0
2014-08-31 08:24:00 0.2 0
2014-08-31 08:24:24 0.2 0
2014-08-31 08:24:46 0.2 0
2014-08-31 08:25:04 0.2 0
2014-08-31 08:25:20 0.2 0
2014-08-31 08:25:37 0.2 0
2014-08-31 08:25:54 0.2 0
2014-08-31 08:26:06 0.2 0
2014-08-31 08:26:15 0.2 0
2014-08-31 08:26:32 0.2 0
2014-08-31 08:26:51 0.2 0
2014-08-31 08:27:03 0.2 0
2014-08-31 08:27:15 0.2 0
2014-08-31 08:27:28 0.2 0
2014-08-31 08:27:42 0.2 0
2014-08-31 08:27:55 0.2 0
2014-08-31 08:28:11 0.2 0
2014-08-31 08:28:25 0.2 0
2014-08-31 08:28:39 0.2 0
2014-08-31 08:28:53 0.2 0
2014-08-31 08:29:08 0.2 0
2014-08-31 08:29:18 0.2 0
2014-08-31 08:29:31 0.2 0
2014-08-31 08:29:47 0.2 0
2014-08-31 08:30:00 0.2 0
2014-08-31 08:30:18 0.2 0
2014-08-31 08:30:32 0.2 0
2014-08-31 08:30:49 0.2 0
2014-08-31 08:31:05 0.2 0
2014-08-31 08:31:22 0.2 0
2014-08-31 08:31:39 0.2 0
2014-08-31 08:31:55 0.2 0
2014-08-31 08:32:09 0.2 0
2014-08-31 08:32:18 0.2 0
2014-08-31 08:32:27 0.2 0
2014-08-31 08:32:36 0.2 0
2014-08-31 08:32:45 0.2 0
2014-08-31 08:33:22 0.2 0
2014-08-31 08:33:39 0.2 0
2014-08-31 08:33:48 0.2 0
2014-08-31 08:34:06 0.2 0
2014-08-31 08:34:27 0.2 0
2014-08-31 08:34:41 0.2 0
2014-08-31 08:35:04 0.2 0
2014-08-31 08:36:58 0.2 0
2014-08-31 08:37:52 0.2 0
2014-08-31 08:38:31 0.2 0
2014-08-31 08:39:05 0.2 0
2014-08-31 08:39:38 0.2 0
2014-08-31 08:40:12 0.2 0
2014-08-31 08:40:38 0.2 0
2014-08-31 08:40:50 0.2 0
2014-08-31 08:41:01 0.2 0
2014-08-31 08:41:28 0.2 0
2014-08-31 08:41:37 0.2 0
2014-08-31 08:41:46 0.2 0
2014-08-31 08:42:04 0.2 0
2014-08-31 08:42:25 0.2 0
2014-08-31 08:42:36 0.2 0
2014-08-31 08:42:50 0.2 0
2014-08-31 08:43:03 0.2 0
2014-08-31 08:43:25 0.2 0
2014-08-31 08:43:47 0.2 0
2014-08-31 08:44:13 0.2 0
2014-08-31 08:44:37 0.2 0
2014-08-31 08:44:54 0.2 0
2014-08-31 08:45:14 0.2 0
2014-08-31 08:45:58 0.2 0
2014-08-31 08:47:25 0.2 0
2014-08-31 08:54:43 0.2 0
2014-08-31 08:56:44 0.2 0
2014-08-31 08:58:20 0.2 0
2014-08-31 08:58:51 0.2 0
2014-08-31 08:59:19 0.2 0
2014-08-31 08:59:54 0.2 0
2014-08-31 09:00:31 0.2 0
2014-08-31 09:01:44 0.2 0
2014-08-31 09:03:41 0.2 0
2014-08-31 09:05:37 0.2 0
2014-08-31 09:06:45 0.2 0
2014-08-31 09:07:35 0.2 0
2014-08-31 09:08:09 0.2 0
2014-08-31 09:08:24 0.2 0
2014-08-31 09:08:39 0.2 0
2014-08-31 09:08:58 0.2 0
2014-08-31 09:09:20 0.2 0
2014-08-31 09:09:42 0.2 0
2014-08-31 09:10:10 0.2 0
2014-08-31 09:10:40 0.2 0
2014-08-31 09:11:05 0.2 0
2014-08-31 09:11:24 0.2 0
2014-08-31 09:11:39 0.2 0
2014-08-31 09:11:56 0.2 0
2014-08-31 09:12:29 0.2 0
2014-08-31 09:13:19 0.2 0
2014-08-31 09:13:57 0.2 0
2014-08-31 09:14:20 0.2 0
2014-08-31 09:14:40 0.2 0
2014-08-31 09:15:04 0.2 0
2014-08-31 09:15:26 0.2 0
2014-08-31 09:15:43 0.2 0
2014-08-31 09:16:01 0.2 0
2014-08-31 09:16:23 0.2 0
2014-08-31 09:16:57 0.2 0
2014-08-31 09:17:25 0.2 0
2014-08-31 09:23:53 0.2 0
2014-08-31 09:24:48 0.2 0
2014-08-31 09:25:29 0.2 0
2014-08-31 09:26:02 0.2 0
2014-08-31 09:26:26 0.2 0
2014-08-31 09:26:48 0.2 0
2014-08-31 09:27:08 0.2 0
2014-08-31 09:27:29 0.2 0
2014-08-31 09:27:53 0.2 0
2014-08-31 09:28:16 0.2 0
2014-08-31 09:28:38 0.2 0
2014-08-31 09:29:02 0.2 0
2014-08-31 09:29:31 0.2 0
2014-08-31 09:29:50 0.2 0
2014-08-31 09:30:10 0.2 0
2014-08-31 09:30:29 0.2 0
2014-08-31 09:30:54 0.2 0
2014-08-31 09:31:16 0.2 0
2014-08-31 09:31:39 0.2 0
2014-08-31 09:34:22 0.2 0
2014-08-31 09:34:51 0.2 0
2014-08-31 09:35:06 0.2 0
2014-08-31 09:35:16 0.2 0
2014-08-31 09:36:08 0.2 0
2014-08-31 09:36:56 0.2 0
2014-08-31 09:37:53 0.2 0
2014-08-31 09:58:37 0.2 0
2014-08-31 10:02:40 0.2 0
2014-08-31 12:16:12 0.2 0
2014-08-31 12:34:54 0.2 0
2014-08-31 13:29:46 0.2 0
2014-08-31 13:52:40 0.2 0
2014-08-31 14:32:00 0.2 0
2014-08-31 14:38:58 0.2 0
2014-08-31 14:42:59 0.2 0
2014-08-31 14:50:12 0.2 0
2014-08-31 15:05:28 0.2 0
2014-08-31 15:25:45 0.2 0
2014-08-31 15:49:25 0.2 0
2014-08-31 16:10:28 0.2 0
2014-08-31 17:26:46 0.2 0
2014-08-31 18:24:37 0.2 0
2014-08-31 18:31:37 0.2 0
2014-08-31 18:39:27 0.2 0
2014-08-31 18:41:31 0.2 0
2014-08-31 18:44:10 0.2 0
2014-08-31 18:48:17 0.2 0
2014-08-31 18:50:58 0.2 0
2014-08-31 18:52:46 0.2 0
2014-08-31 18:55:23 0.2 0
2014-08-31 19:00:23 0.2 0
2014-08-31 19:04:27 0.2 0
2014-08-31 19:07:12 0.2 0
2014-08-31 19:10:45 0.2 0
2014-08-31 19:13:40 0.2 0
2014-08-31 19:19:03 0.2 0
2014-08-31 19:25:23 0.2 0
2014-08-31 19:34:27 0.2 0
2014-08-31 19:44:11 0.2 0
2014-08-31 20:00:15 0.2 0
2014-08-31 20:01:15 0.2 0
2014-08-31 20:01:40 0.2 0
2014-08-31 20:01:53 0.2 0
2014-08-31 20:02:07 0.2 0
2014-08-31 20:02:26 0.2 0
2014-08-31 20:02:58 0.2 0
2014-08-31 20:03:42 0.2 0
2014-08-31 20:04:22 0.2 0
2014-08-31 20:04:58 0.2 0
2014-08-31 20:05:28 0.2 0
2014-08-31 20:06:02 0.2 0
2014-08-31 20:08:01 0.2 0
2014-08-31 20:11:21 0.2 0
2014-08-31 20:13:14 0.2 0
2014-08-31 20:14:53 0.2 0
2014-08-31 20:16:32 0.2 0
2014-08-31 20:18:32 0.2 0
2014-08-31 20:20:26 0.2 0
2014-08-31 20:22:43 0.2 0
2014-08-31 20:26:41 0.2 0
2014-08-31 20:30:14 0.2 0
2014-08-31 20:33:32 0.2 0
2014-08-31 20:36:54 0.2 0
2014-08-31 20:41:37 0.2 0
2014-08-31 20:42:58 0.2 0
2014-08-31 20:43:46 0.2 0
2014-08-31 20:44:35 0.2 0
2014-08-31 20:47:10 0.2 0
2014-08-31 20:56:03 0.2 0

This is my code so far:

library(xts)

## Import data from txt file
tip_time <- read.table("../Rainfall/Malmo_regndata/fasta/M01_Turbinen_vippning.txt", header = TRUE, check.names=FALSE, sep = "\t", skip = 1)
tip_time$Time <- as.POSIXct(tip_time$Time) # Convert to POSIXct
tip_time = xts(tip_time[,-1], order.by=tip_time[,1]) # Convert to xts
acc_tip <- cumsum(tip_time[,1]) # Accumulated rainfall (here in mm)

## Make time series with regular time steps
step <- 5
days <- 1
n <- days*24*60/step
timesteps <- ISOdatetime(2014,08,31,0,0,0) + seq(0:(n-1))*step*60  # Make timesteps
ts <- xts(rep(NA,n), order.by=timesteps) # Make xts with timesteps and NA

## Merge data into time series with regular time steps
ts_tip <- merge(ts, na.locf(merge(ts, acc_tip)[,2]), join="inner")[,2] # Merge acc_tip with ts
ts_tip[is.na(ts_tip)] <- 0 # Make 0 of NA

## Calculate intesities from accumulated rainfall
intensity <- diff(ts_tip, lag = 1) # Calculate intensities (here in mm/5 min)
intensity[is.na(intensity)] <- 0 # Make 0 of NA

plot(intensity, main="rainfall intensity [mm/5 min]")

Between 10.00 and 18.00, the rainfall intensity was mostly lower than 0.2 mm. This means that we need to smoothen the time series out. Every 0.2 mm of rainfall should be distributed evenly among the time steps before, if there is one or more time steps without any tip, as we assume that it the rain fell evenly during these time steps. How can this be achieved in R? I am grateful if anyone has a good idea on how to solve this.

This is a small example from the textbook Afløbsteknik by Winther et al. (2011, Polyteknisk forlag, Lyngby). It shows the desired result (tip_corrected). Note that the first registrated tip stays the same, while the smoothing takes place during the rainfall. There are no smoothing between rainfall events. One could assume that there should be 2 hours between two rainfall events to make them individual rainfall events.

tip<-c(1,rep(0,9),2,1,2,0,0,1,rep(0,14),1)
tip_corrected<-c(1,rep(0.1,9),1.1,1,2,0.333,0.333,0.333,rep(0.0667,15))

windows()
plot(tip, pch = 1)
points(tip_corrected, pch = 4)
legend(23,2, legend = c("tip", "tip_corrected"), pch = c(1,4))

Perhaps you could create a smaller example, and show us the corresponding desired output. E.g. given input like `df <- data.frame(time = 1:10, rain = c(0.2, NA, NA, 0.2, 0.2, NA, 0.2, NA, NA, NA))`, I expect bla bla bla. — Henrik, Aug 19 '15 at 13:19
Strikes me you can make one of two assumptions: 1) (as stated) that the 0.2 mm of precipitation is spread evenly over the time series since the last tip. 2) that the 0.2 mm only fell in the single time step preceding the tip. With a depth of 0.2 mm is it really going to matter which you pick? Do the WMO (World Meteorological Office) have a standard approach? — MikeRSpencer, Aug 19 '15 at 13:30
In terms of solving it, I'd use a database like SQLite; writing the raw data to a table and then using SQL to create a regular time series from it in a different table. You can interface with SQLite direct from R, a big advantage is you'll only need the data prep step once, not each time you load it. — MikeRSpencer, Aug 19 '15 at 13:34
What about using `loess()`, either on the whole series or, via `subset`, only on the low-rainfall spells? — ulfelder, Aug 19 '15 at 13:49
I have added a small example now – thank you for advice, @Henrik. — Johanna Sörensen, Aug 20 '15 at 09:39
No problem! In general, people are much more willing to help if you provide a truly _minimal_ example, both when it comes to removing code which is redundant for the actual problem, and presenting a data set as small as possible to capture the essence of your problem. I highly recommend to read [**here**](http://stackoverflow.com/help/mcve), [**here**](http://www.sscce.org/), [**here**](http://adv-r.had.co.nz/Reproducibility.html), and [**here**](http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example/5963610#5963610). — Henrik, Aug 20 '15 at 10:13
Sorry but could you please clarify your logic when "smoothing" the values. Consider the first run of zeros in "tip", where the first following non-zero element is two. As I understood you, the 2 should be distributed evenly on its own index, and the preceeding 9 zeros. 2 / 10 = 0.2. But in "tip_corrected" there are 9 0.1:s. And what is the logic behind the 1.1 on index 11? I haven't bothered about the rest of the vector yet... — Henrik, Aug 20 '15 at 11:18
The logic is that if there are two registered tips on timestep 11, the water collected for one of the tips might have fallen during timestep 2 to 11. Collection of water for the other tip must have taken taken place during the timestep (11). Does it make sence to you? Some things are obvious when you work within the field, but not when you work with something different. It is not very easy to describe it with just text. — Johanna Sörensen, Aug 20 '15 at 12:11

score 2 · Answer 1 · answered Aug 19 '15 at 15:34

If I understand what you're trying to do, rather than doing the merge for ts_tip, you could use the approx function with suitable rules to linearly interpolate cumulative rainfall at the regularly spaced times. rule=1:2 leaves NA's in the series prior to first rainfall and fills the values past the last acc_tip time with the last acc_tip value as shown below. The remainder of your code is as before.

   ## Merge data into time series with regular time steps
    # ts_tip <- merge(ts, na.locf(merge(ts, acc_tip)[,2]), join="inner")[,2] # Merge acc_tip with ts
    # ts_tip[is.na(ts_tip)] <- 0 # Make 0 of NA

    #
    # interpolation of cumulative rainfall at equi-spaced times using approx function
    ts_tip <- xts(approx(index(acc_tip), acc_tip, rule=1:2, xout=index(ts))$y, order.by=index(ts))
    ts_tip[is.na(ts_tip)] <- 0 # changes NA's at start of series to 0's

Thank you for a good try, but the rain is coming to late in this case. We must assume that the rain fell _before_ it was registered. — Johanna Sörensen, Aug 20 '15 at 09:11

score 2 · Answer 2 · answered Aug 20 '15 at 16:16

This is probably not the most elegant way and I would be glad to see better solutions, but the following should work:

library(xts)
library(plyr)

## Import data from txt file
## I copied your data dump to dat.txt and added "Date" as first column name. (I import 4 columns and merge "Date" and "Time" afterwards.)
tip_time <- read.table("dat.txt", header = TRUE,
                       sep = " ", stringsAsFactors = FALSE)
tip_time$Time <- paste(tip_time$Date, tip_time$Time)
tip_time[,"Date"] <- NULL
tip_time$Time <- as.POSIXct(tip_time$Time) # Convert to POSIXct
colnames(tip_time) <- c("Time", "bucket", "Flag")

## Make "time series" with regular time steps.
regularSteps <- data.frame(
  Time =
    seq(from = trunc(tip_time[1, 1], "day"),
        to = trunc(tail(tip_time[, 1], n = 1), "day") + 60*60*24 - 1,
        by = 1))

tip_regular <- merge(regularSteps, tip_time, by = "Time", all = TRUE)
tip_regular[is.na(tip_regular)] <- 0

## To aggregate, create groups of 5 minutes.
tip_regular$group <- floor(as.numeric(tip_regular$Time) / (5*60))

res <- ddply(.data = tip_regular, .variables = "group", .fun = function(x) {
  return(data.frame(Time = tail(x$Time, n = 1), buckets = sum(x$bucket)))
})[, -1]

# To check the result afterwards:
res$original <- res$buckets

# Smoothing:
bucketsize <- 0.2

while(any(res$buckets == 0)) { # Do the following as long as there are empty buckets (or until all empty buckets are at the end of the data set.)

  # These 3 lines could probably be simplified:
  firstEmpty <- which(res$buckets == 0)[1]
  allFull <- which(res$buckets != 0)
  firstFullAfterEmpty <- allFull[allFull > firstEmpty][1]

  if(is.na(firstFullAfterEmpty)) break

  # Take one bucket out, this bucket will be redistributed:
  res[firstFullAfterEmpty, "buckets"] <- res[firstFullAfterEmpty, "buckets"] - bucketsize

  toFill <- firstFullAfterEmpty - firstEmpty + 1 # # Number of buckets to fill
  res[firstEmpty:firstFullAfterEmpty, "buckets"] <-  bucketsize / toFill # equally redistribute the water
}

tip_ts <- xts(x = res$buckets, order.by = res$Time)
plot(tip_ts, main="rainfall intensity [mm/5 min]")

A. Webb · Answer 3 · 2015-08-20T17:36:43.513

I'm using the small textbook example you provided, where tip has the original data and tip_corrected the desired data (to 3 decimal places).

First, find runs of rainfall activity

r<-rle(as.numeric(tip>0))

Allocation to runs of zeros

ind<-r$values==0 
r$values[ind]<-1/(1+r$length[ind])
r$values[!ind]<-0
tip2<-tip+inverse.rle(r)

Locations in tips to borrow from

idx<-cumsum(r$lengths)[which(ind)]+1 
tip2[idx] <- tip2[idx]-1+tip2[idx-1]

Test

all.equal(round(tip2,3),round(tip_corrected,3))
#> TRUE

You'll need to handle edge cases of first or last entry as a 0 as would be appropriate for your purposes. It would also seem appropriate to have a cut-off for the length of zero runs to allocate to as it does not rain all of the time.

Rainfall intensity from a tipping bucket

3 Answers3