-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathChapter_12_Extremes.qmd
472 lines (348 loc) · 25.1 KB
/
Chapter_12_Extremes.qmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
# Extremes
## Introduction
Starting with daily, or sub-daily data the analysis proceeds in two
stages. The first is to get the extremes and the second is to analyse
them. The data from two stations in Ghana are used for illustration. Use
***File \> Open from Library \> Instat \> Browse \> Climatic \> Ghana***
and open the RDS file called ***Ghana two stations***. From Fig 11.1a we
see the data start in 1944, though the elements, other than rainfall
start later.
----------------------------------------------------------------------------------------------------------
***Fig. 11.1a Two stations from Ghana*** ***Fig. 11.1b***
---------------------------------------------------- -----------------------------------------------------
{width="3.032425634295713in" {width="2.950962379702537in"
height="2.8353412073490816in"} height="2.535641951006124in"}
----------------------------------------------------------------------------------------------------------
In the Climatic menu the data are already in the right "shape" and there
is a date column, see Fig. 11.1a. So start by checking whether there are
any missing dates to infill, Fig. 11.1b.
----------------------------------------------------------------------------------------------------------
***Fig. 11.1c*** ***Fig. 11.1d***
---------------------------------------------------- -----------------------------------------------------
{width="3.032425634295713in" {width="2.950962379702537in"
height="2.8353412073490816in"} height="2.535641951006124in"}
----------------------------------------------------------------------------------------------------------
In ***Climatic \> Dates Infill Missing Dates***, include the
***Station***, Fig. 11.1c. The results, in Fig. 11.1d, indicate that
there were 5 missing months in the record at Saltpond and four at
Tamale. There are now 53297 rows of data.
Now use ***Climatic \> Dates \> Use Date***, Fig. 11.1e, and complete as
shown.
Then use Climatic \> Define Climatic data. It should complete
automatically. Check for uniqueness and then press OK.
---------------------------------------------------------------------------------------------------------
***Fig. 11.1e*** ***Fig. 11.1f***
--------------------------------------------------- -----------------------------------------------------
{width="2.28207895888014in" {width="3.4914720034995628in"
height="3.2165966754155733in"} height="4.148623140857393in"}
---------------------------------------------------------------------------------------------------------
Now use ***Climatic \> Check Data \> Inventory***, Fig. 11.1g. Include
the elements down to wind speed.
----------------------------------------------------------------------------------------------------------
***Fig. 11.1g*** ***Fig. 11.1h***
---------------------------------------------------- -----------------------------------------------------
{width="2.729400699912511in" {width="3.3204877515310587in"
height="3.16913823272091in"} height="3.202425634295713in"}
----------------------------------------------------------------------------------------------------------
The results show the other elements started roughly in 1960. There are
relatively few missing values in the rainfall, and the other elements
are also reasonably complete.
The same Climatic \> Check Data menu has options for quality control
checks. These are assumed, as we proceed to examine the extremes.
## Getting the extremes
In the ***Climatic \> Prepare*** menu there are four dialogues that get
extremes. They are considered briefly and then ***Climatic \> Prepare \>
Extremes*** is examined in detail.
The ***Climatic \> Prepare \> Climatic Summaries***, Fig. 11.2b has
already been used extensively in this guide.
-----------------------------------------------------------------------------------------------------------
***The ClimzaFig. 11.2a*** ***Fig. 11.2b***
----------------------------------------------------- -----------------------------------------------------
{width="2.9926891951006125in" {width="2.9134219160104986in"
height="3.2375459317585302in"} height="3.1352055993000874in"}
-----------------------------------------------------------------------------------------------------------
In Fig. 11.2c we can choose the extremes, i.e. the minimum and/or
maximum. These can be annual, as shown in Fig. 11.2b, or for a part of
the year, or perhaps monthly.
-----------------------------------------------------------------------------------------------------------
***Fig. 11.2c*** ***Fig. 11.2d***
----------------------------------------------------- -----------------------------------------------------
{width="2.8620866141732284in" {width="2.8025732720909886in"
height="3.151451224846894in"} height="3.2878444881889766in"}
-----------------------------------------------------------------------------------------------------------
Fig. 11.2d shows the ***Climatic \> Prepare \> Spells*** dialogue. This
automatically gives the extreme, i.e. longest spell each year. This may
be the longest dry spell for rainfall, or the longest hot (or cold)
spell for temperatures, etc.
The Climdex system is covered in Sections 11.3 and 11.4. Hence now
consider ***the Climatic \> Prepare \> Extremes*** dialogue, Fig. 11.2e.
---------------------------------------------------------------------------------------
***Fig. 11.2e*** ***Fig. 11.2f***
--------------------------------------------------- -----------------------------------
{width="2.98702646544182in"
height="4.1097736220472445in"}
---------------------------------------------------------------------------------------
[To be continued]{.mark}
## Climdex Indices - precipitation
A set of 27 climate change indices have resulted from WMO meetings and
reports. They are described in
[[http://etccdi.pacificclimate.org/list_27_indices.shtml]{.underline}](http://etccdi.pacificclimate.org/list_27_indices.shtml)
and implemented through an R package called climdex.pcic. The pcic
stands for Pacific Islands Impacts Consortium, but the indices are
general.
Each index can produce an annual summary, and some offer the option of
monthly summaries. The are a single dialogue in R-Instat. Sixteen of the
indices are temperature-based. The other 11 are rainfall indices.
The Dodoma data from Tanzania are used for illustration. Use ***File \>
Open from Library \> Instat \> Browse \> Climatic \> Tanzania*** and
open the file called Dodoma.rds. It is already defined as a climatic
dataset. Hence the climatic dialogues can be used immediately.
The annual summaries from climdex are compared with those used in
Chapters 6 and 7. Hence start with the ***Climatic \> Prepare \>
Climatic Summaries***, Fig. 11.3b.
----------------------------------------------------------------------------------------------------------
***Fig. 11.3a*** ***Fig. 11.3b***
---------------------------------------------------- -----------------------------------------------------
{width="3.153367235345582in" {width="2.8408005249343833in"
height="3.609623797025372in"} height="3.593584864391951in"}
----------------------------------------------------------------------------------------------------------
Press ***Summaries*** on the main dialogue and choose the summaries
indicated in Fig. 11.3c. Then choose the ***Missing Options*** tab to
give Fig. 11.3d. The default in climdex is to set the summary to missing
if more than 15 days in the year are missing, so the same is done here.
---------------------------------------------------------------------------------------------------------
***Fig. 11.3c*** ***Fig. 11.3d***
---------------------------------------------------- ----------------------------------------------------
{width="3.008050087489064in" {width="2.982723097112861in"
height="2.9473370516185478in"} height="2.1991699475065616in"}
---------------------------------------------------------------------------------------------------------
The result is two annual summaries, Fig. 11.3e, that are like two of the
climdex indices. They are ready to draw graphs, fir trend lines and so
on. The data frame, in Fig. 11.3e, has 79 rows, because there are 79
years of data
Use ***Climatic \> Prepare \> Climdex***, Fig. 11.3f. The dialogue
should fill automatically. If not, then check you are using the correct
data frame.
----------------------------------------------------------------------------------------------------------
***Fig. 11.3e*** ***Fig. 11.3f***
---------------------------------------------------- -----------------------------------------------------
{width="2.275330271216098in" {width="3.6112981189851268in"
height="3.5917311898512687in"} height="3.6112981189851268in"}
----------------------------------------------------------------------------------------------------------
In Fig. 11.3f click on ***Indices***. Complete the settings as shown in
Fig. 11.3g and then choose the ***precipitation tab***. The numbers for
each index match those given in
[[http://etccdi.pacificclimate.org/list_27_indices.shtml]{.underline}](http://etccdi.pacificclimate.org/list_27_indices.shtml)
. For illustration***, tick everything*** there and press ***Return***.
------------------------------------------------------------------------------------------------------------
***Fig. 11.3g*** ***Fig. 11.3h***
----------------------------------------------------- ------------------------------------------------------
{width="3.097315179352581in" {width="2.8853073053368328in"
height="2.6226126421697287in"} height="2.862516404199475in"}
------------------------------------------------------------------------------------------------------------
This results in 11 further columns, for each of the precipitation
indices. They are added to the yearly data frame and shown in Fig.
11.3i. Each is described briefly, before continuing with the analysis.
-----------------------------------------------------------------------
***Fig. 11.3i***
-----------------------------------------------------------------------
{width="6.155778652668417in"
height="2.999458661417323in"}
-----------------------------------------------------------------------
The indices are defined as shown in table 11.3a. In Fig. 11.3i the
variable max_rain, from the Climatic \> Prepare \> Climatic Summaries is
seen to be the same as Rx1day. We consider briefly how to get each of
these indices using the other R-Instat dialogues.
---------------------------------------------------------------------------------
***Table 11.3a
Precipitation
indices from
climdex***
--------------- ------------ ----------------------------------------------------
***Number*** ***Name*** ***Description***
17 Rx1day Annual maximum
18 Rx5day Maximum from 5-day running totals
19 SRII Simple intensity index, i.e. Annual total/Number of
rain days
20 R10mm Annual number of rain-days with 10mm or more
21 R20mm Annual number of rain-days with 20mm or more
22 Rnnmm Annual number of days with ≥ nn(mms). User chooses
value of nn
23 CDD Longest dry spell in the year (dry is \<1mm)
24 CWD Longest spell of successive rain days (rain is
\>=1mm)
25 R95p Annual total greater than 95^th^ percentile in base
period
26 R99p Ditto for 99^th^ percentile
27 PRCPTOT Total annual rainfall (from days with ≥ 1mm)
---------------------------------------------------------------------------------
This comparison is partly to help users understand exactly what each
index is measuring. In addition the regular dialogues provide additional
flexibility, if needed to examine the indices in more detail.
The second summary, produced earlier is the total annual rainfall,
called sum_rain in Fig. 11.3i. This is almost the same as the climdex
index 27, PRCPTOT. For example sum_rain = 523mm in 1935, compared to
514mm for PRCPTOT.
The small difference is because the sum_rain has totalled all the rain
days, while PRCPTOT only considers those with at least 1mm.
Check this with ***Prepare \> Column: Calculate \> Calculation***. With
the ***Logical keyboard*** make a new column, called rain1, Fig. 11.3j,
with:
rain1 \<- ***ifelse(rain\<1, 0, rain)***, or equivalently rain1 \<-
***(rain\>=1) \* rain***.
Then use ***Climatic \> Prepare \> Climatic Summaries*** with the new
***rain1*** variable to check the annual totals now agree with those
from climdex.
------------------------------------------------------------------------------------------------------------
***Fig. 11.3j*** ***Fig. 11.3k***
------------------------------------------------------ -----------------------------------------------------
{width="3.2370570866141732in" {width="2.731232502187227in"
height="2.3834208223972in"} height="3.5022265966754156in"}
------------------------------------------------------------------------------------------------------------
From the rain5 variable, the ***Climatic \> Prepare \> Extremes*** is an
alternative dialogue to give the annual maxima, Fig. 11.3l. This gives
the same results as the climdex Rx5day variable. It also gives a further
the day in the year of the maximum. This could be used in a study to
investigate whether there is any evidence for a trend in ***when the
maximum occurs*** as well as its value.
------------------------------------------------------------------------------------------------------------
***Fig. 11.3l*** ***Fig. 11.3m***
------------------------------------------------------ -----------------------------------------------------
{width="3.1908333333333334in" {width="2.838053368328959in"
height="4.309553805774279in"} height="2.913501749781277in"}
------------------------------------------------------------------------------------------------------------
The "Simple intensity index", SRII is essentially the mean rain per rain
day, (just using the values of days with more than 1mm). In Fig. 11.3i
it is just PRCPTOT/Rnnmm, because we chose 1mm as the threshold. For
example, in 1935 there were 36 rain days with a total of 514mm. Hence
SRII~1935~ = 514/36 = 14.26mm
The next 2 indices, R10mm and R20mm are just the number days each year
with 10mm, and 20mm or more, each year. They can also be given using the
***Climatic \> Prepare \> Climatic Summaries*** dialogue.
The indices CDD and CWD give the maximum dry-spell length and rain-spell
lengths, where rain = 1mm. They are special cases of the ***Climatic \>
Prepare \> Spells*** dialogue, Fig. 11.3n. The data in Fig. 11.3i show
that the CDD index for the whole calendar year is probably of little
interest, for this site, because the months of May to October are
usually dry. Hence the longest dry-spell of 197 days, in 1935, is not a
surprise. However, assessing evidence for trends in the longest
dry-spell during the season, perhaps from 1 January to 31 March, may be
useful.
----------------------------------------------------------------------------------------------------------
***Fig. 11.3n Spells dialogue to give CWD index*** ***Fig. 11.3o Filter sub-dialogue for rain days in
baseline years***
---------------------------------------------------- -----------------------------------------------------
{width="2.80285542432196in" {width="3.185751312335958in"
height="3.4301082677165353in"} height="3.2739555993000873in"}
----------------------------------------------------------------------------------------------------------
The final 2 precipitation indices are R95p and R99p. They are the total
rainfall each year from heavy rain days. The definition of "heavy" is
relative to the baseline years. The first step is therefore to find the
thresholds. The process is as follows:
1. ***Filter*** the Dodoma data to the baseline years and just the rain
days, Fig. 11.3.
2. Use the ***Prepare \> Column: Calculate \> Column Summaries***, Fig.
11.3p, with the ***percentile summary***, Fig. 11.3q, to give the
95% and 99% points of the rain variable. The 95% point, Fig. 11.3q,
= 45.57mm and the 99% point = 67.3mm
----------------------------------------------------------------------------------------------------------
***Fig. 11.3p*** ***Fig. 11.3q***
---------------------------------------------------- -----------------------------------------------------
{width="2.959998906386702in" {width="3.185751312335958in"
height="3.4301082677165353in"} height="3.2739555993000873in"}
----------------------------------------------------------------------------------------------------------
3. Now ***filter*** to use just the days for the whole record where
(rain \> 45.57), Fig. 11.3r. .
4. ***Use Climatic \> Prepare \> Climatic Summaries*** to give the sum
and number of observations, Fig. 11.3s
--------------------------------------------------------------------------------------------------------------
***Fig. 11.3r*** ***Fig. 11.3s***
------------------------------------------------------ -------------------------------------------------------
{width="2.996907261592301in" {width="2.6710126859142607in"
height="3.2817366579177603in"} height="3.5565507436570427in"}
--------------------------------------------------------------------------------------------------------------
The resulting data are in Fig. 11.3t. The new sum_rain variable gives
the same values as the R95p. In the first year, the total was 210.3mm
from 3 rain days.
-----------------------------------------------------------------------
***Fig. 11.3t***
-----------------------------------------------------------------------
{width="3.06751968503937in"
height="3.325728346456693in"}
-----------------------------------------------------------------------
## Climdex -- Temperatures
The 16 temperature indices are shown in Table 11.4a.
--------------------------------------------------------------------------------
***Table 11.4a
Temperature
indices from
climdex***
-------------- ------------ ----------------------------------------------------
***Number*** ***Name*** ***Description***
1 FD Number of frost days, when daily minimum
temperature, Tn \<0.
2 SU Number of "Summer" days, when daily maximum
temperature, Tx \> 25
3 ID Number of icing days, when Tx \< 0
4 TR Number of tropical nights, when Tn \> 20
5 GSL Growing season length. Number of days between first
span of 6 consecutive days with daily Tmean \> 5°C
and first span of 6 days (after July 1^st^) with
Tmean \< 5°C. (July to June in Southern hemisphere.)
6 TXx Annual or monthly maximum of Tx
7 TNx Annual or monthly maximum of Tn
8 TXn Annual or monthly minimum of Tx
9 TNn Annual or monthly minimum of Tn
10 TN10p Percentage of days when Tn \< 10^th^ percentile from
the baseline
11 TX10p Ditto for Tx \< 10^th^ percentile
12 TN90p Ditto for Tn \> 90^th^ percentile
13 TX90p Ditto for Tx \> 90^th^ percentile
14 WSDI Warm spell duration index, the annual number of day
where at least 6 consecutive days are warmer than
the 90^th^ percentile
15 CSDI Cold spell duration index, the annual number of days
when at least 6 consecutive days are colder than the
10^th^ percentile
16 DTR Mean temperature range, i.e. mean difference between
Tx and Tn
--------------------------------------------------------------------------------
They are again illustrated with the Dodoma data. Use Climatic \> Prepare
\> Climdex, Fig. 11.4a and complete the Temperature sub-dialogue as
shown in Fig. 11.4b.
--------------------------------------------------------------------------------------------------------------
***Fig. 11.4a The Climdex dialogue*** ***Fig. 11.4b Climdex temperature sub-dialogue***
------------------------------------------------------ -------------------------------------------------------
{width="2.3313899825021873in" {width="3.7590102799650045in"
height="2.152358923884514in"} height="2.7697976815398073in"}
--------------------------------------------------------------------------------------------------------------
The results are in Fig. 11.4c. Some results are obvious; in particular
in the later years, shown in Fig. 11.4c, there are about 30% of days per
year in TN90p, i.e. with Tn higher than the 90% point from the 1961-90
baseline. And TN10p has very low values. The change in Tn is clearer
than that of the maximum temperatures, Tx.
-----------------------------------------------------------------------
***Fig. 11.4c***
-----------------------------------------------------------------------
{width="6.069974846894138in"
height="3.988590332458443in"}
-----------------------------------------------------------------------
As in Section 11.3, some of the temperature indices can be calculated
through the ***Climatic \> Prepare \> Climatic Summaries*** dialogue.
For example completing Fig. 11.4d and Fig. 11.4e as shown produces the
indices TNn and TNx.
--------------------------------------------------------------------------------------------------------------
***Fig. 11.4d*** ***Fig. 11.4e Choosing the max and min***
------------------------------------------------------ -------------------------------------------------------
{width="3.0453029308836395in" {width="2.8903346456692915in"
height="3.371376859142607in"} height="2.777569991251094in"}
--------------------------------------------------------------------------------------------------------------
The calculations for 6 of the indices is more complex. They are numbered
10 to 15 in Table 11.4a and depend on the temperatures in the baseline
period, usually 1961 to 1990. In this case the 10% and 90% points are
found, in turn, for each day of the year[^48] and these values are then
compared with the temperature on that day for the record.
## Using the climdex indices
[To be completed]{.mark}
## Extreme value analysis
[Using the extRemes package]{.mark}