From 3e5cc5b4a467db7f5355c98140771654dc69468a Mon Sep 17 00:00:00 2001 From: Bewa Date: Wed, 31 Jul 2024 21:42:53 +0300 Subject: [PATCH] Add files via upload --- Chapter_20_Climate_Normals.qmd | 1302 ++++++++++++++++---------------- 1 file changed, 634 insertions(+), 668 deletions(-) diff --git a/Chapter_20_Climate_Normals.qmd b/Chapter_20_Climate_Normals.qmd index 204b220..c0435d3 100644 --- a/Chapter_20_Climate_Normals.qmd +++ b/Chapter_20_Climate_Normals.qmd @@ -1,669 +1,635 @@ -# Climate Normals -## Introduction - -The calculation of climate normals in this chapter is based largely on -(World Meteorological Organization (WMO), 2017). We also consider the -adaptation of the guidelines to the calculations of the normals in the -US, as described in (Arguez, et al., 2012). - -A climatological standard normal now refers to the most recent 30-year -period finishing in a zero, i.e. currently 1981-2010, and soon to be -1991-2020. In addition, the 1961-1990 period is retained as a standard -reference period for assessing long-term climate change. - -A distinction is made in (World Meteorological Organization (WMO), -2017), between "Principal Climatological Parameters" and "Secondary -Parameters". There are 8 primary parameters including monthly total -rainfall (precipitation) and the total number of rain days, Table 19.1a. - - ----------------------------------------------------------------------- - ***Table 19.1a WMO Principal Climatological - Parameters*** - ------------------------------------------------------- --------------- - **Parameter** **Units** - - Precipitation total mm - - Precipitation days (Precip ≥ 1mm) days - - Mean Tmax °C - - Mean Tmin °C - - Mean Tavg °C - - Mean sea-level pressure hPa - - Mean vapour pressure hPa - - Total hours of sunshine hours - ----------------------------------------------------------------------- - -The quintile boundaries for rainfall (mm) and the mean number of days -with more than 5, 10, 50, 100 and 150mm are secondary parameters. -Temperature thresholds and extremes are also included. - -These are intended as guidelines and are adapted by individual -countries. Examples from the US are shown in Table 19.1b. This table is -adapted from Table 5 in (Arguez, et al., 2012). The units have been -changed to millimetres for rainfall and °C for temperatures (US uses -inches and Fahrenheit.) - - -------------------------------------------------------------------------------------------------------- - Table 19.1b - Monthly and - annual - normals for - a station in - Chicago, - from - (Arguez, et - al., 2012) - ------------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------- - Variable J F M A M J J A S O N D Ann - - Tmax (°C) -0.3 2.1 8.2 15.1 21.2 26.6 29.0 27.8 24.1 17.1 9.2 1.8 15.2 - - Tavg (°C) -4.0 -1.8 3.8 10.2 16.1 21.7 24.4 23.4 19.1 12.3 5.3 -1.7 10.8 - - Tmin (°C) -7.7 -5.7 -0.6 5.4 10.9 16.7 19.7 19.0 14.2 7.6 1.4 -5.2 6.4 - - DTR (°C) 7.4 7.8 8.8 9.7 10.3 9.9 9.3 8.8 9.9 9.5 7.8 7.0 8.8 - - Precip(mm) 52 49 69 92 105 103 102 101 84 82 87 65 993 - - HDD 692 564 451 249 104 17 1 2 43 194 391 620 3327 - - CDD 0 0 1 7 34 117 188 160 66 9 0 0 581 - - Days Tmax \> 0 0 0 0 0.6 3.1 6.3 3.8 1.2 0 0 0 15.1 - 32.2 - - Days with 1.4 2.9 10.6 23.5 30.5 30 31 31 30 28.1 13.1 2.9 235 - Tmin \< 10 - - Precip 25% 29 26 41 54 63 70 53 57 40 49 48 38 - - Precip 75% 75 66 90 119 141 124 115 143 117 93 133 80 - - Precip \> 10.7 8.8 11.2 11.1 11.4 10.3 9.9 9 8.2 10.2 11.2 11.1 123.1 - 0.2mm[^59] - - Precip \> 0.2 0.2 0.3 0.9 1 1.3 1 1.3 0.7 0.8 0.8 0.5 9 - 25mm - -------------------------------------------------------------------------------------------------------- - -One differences is for rainfall, where WMO suggests quintiles, i.e. 20%, -to 80%, while the US uses quartiles (25% and 75%). Heating (HDD) and -cooling degree days are also including. A heating degree day is defined -as a value of Tavg above 18°C (65 degrees Fahrenheit), while CDDs are -temperatures below that level. - -The WMO lower threshold for rainfall is proposed as ≥ 1mm. We have -largely used 0.85mm as a practical lower limit in this guide. We claim -this is consistent with the WMO value of ≥1mm. For practical purposes, -as data are recorded to 0.1mm the WMO value is effectively \> 0.95mm. -For consistency between stations (which is important for climate -normals) the value of 0.85mm is about the same. But it allows for -differences in rounding at different stations. This can occur in 2 ways. -If data were originally in inches, then 0.01inch = 0.3mm. The value of -0.9mm is not possible, because 0.03inches = 0.8mm, while 0.04inches = -1mm. - -In addition, some observers round data more than others. An observer who -rounds 0.9mm to 1mm would have that day counted as rain, while the more -precise observer, recording the same value as 0.9mm would have it -omitted as dry. - -For these reasons, we claim the proposed threshold value of 0.85mm is a -practical was of implementing the WMO ≥1mm threshold. - -+-----------------------------------+-----------------------------------+ -| ***Fig. 19.1a Inventory for | ***Fig. 19.1b Subset with 30 | -| Dodoma*** | years*** | -| | | -| ***Climatic \> Check Data \> | Right-click \> Filter (to year | -| Inventory*** | from 1981 to 2010) | -+===================================+===================================+ -| ![](media/image320. | ![](media/image326. | -| png){width="2.9576673228346455in" | png){width="2.8694127296587926in" | -| height="2.9941371391076115in"} | height="3.0189227909011374in"} | -+-----------------------------------+-----------------------------------+ - -In principle, producing normals is straightforward as is shown in -Section 19.2 with examples using rainfall data. Complications relate -largely to the presence of missing values in the reference period and -this is discussed in Section 19.3. - -The Dodoma data are used as an example. ***File \> Open from Library \> -Instat \> Browse \> Climatic \> Tanzania \> Dodoma.rds***. - -The data are already defined as climatic. An inventory is shown in Fig. -19.1a. IT shows there are virtually no missing values in the rainfall, -either in the 30 years from 1961 or in the most recent period, from 1981 -to2010. A subset of the data is produced as shown in Fig. 19.1b, and -rainfall normals from 1981-2010 are shown in Section 19.2. - -There are also relatively few missing values in the temperatures. They -are considered in Section 19.3, where we also explain the WMO -recommendations for coping with missing values. - -The sunshine records only started in 1973, and so could not be used for -1961-90 normals. And there are far too many missing values for them to -be used in 1981-2010, unless they can be merged with satellite data. -This is considered in Section 19.4. - -The examples here are for a single station. Usually they would be done -for a whole set of stations in a single file, and that is no more work. -The process, in R-Instat, currently involves three successive steps. -There seems to be no R-package for this task. We expect to construct one -for R and hence R-Instat, in the future. - -## Precipitation normals - -From Fig. 19.1b the Dodoma data are now from 1981 to 2010. We have -chosen to keep the year from January to December, though there could be -a case for July to June, as that would mean each "year" would be a -complete season. The rains in Dodoma are from November to April. In -(World Meteorological Organization (WMO), 2017), mention is made of -climate normals being for seasons rather than annual, but no details are -given, In Tanzania part of the country is unimodal and part is bimodal, -so comparisons of the normals between stations would be easier with a -consistent definition and January to December therefore seems justified. - -The first 2 normals in Table 19.1a are the precipitation totals and the -number of rain days. As preparation, calculate the rain days as shown in -Fig. 19.2a. In Fig. 19.2a the 0.85mm threshold has been used, which we -claimed above, is consistent with the WMO definition of rain ≥ 1mm. (Use -0.95mm is you don't agree!) - -+--------------------------------+-------------------------------------+ -| ***Fig. 19.2a Add a variable | ***Fig. 19.2b*** | -| for raindays*** | | -| | | -| ***Climatic \> Prepare \> | | -| Transform*** | | -+================================+=====================================+ -| ![](media/image343.png | ![](media/image32 | -| ){width="2.7958967629046367in" | 2.png){width="3.2288713910761153in" | -| height="3.432683727034121in"} | height="3.409433508311461in"} | -+--------------------------------+-------------------------------------+ - -The resulting daily data are in Fig. 19.2b. The rainday variable can be -seen to be 1 on rain days, and 0 otherwise. - -Getting the monthly normals is a 2-step process and the annual normals -adds a 3rd step. - -The first step uses the ***Climatic \> Prepare \> Climatic Summaries***, -as shown in Fig. 19.2c, to give the monthly rainfall totals for each -year. - -+-----------------------------------+----------------------------------+ -| ***Fig. 19.2c*** | ***Fig. 19.2d*** | -| | | -| ***Climatic \> Prepare \> | | -| Climatic Summaries*** | | -+===================================+==================================+ -| ![](media/image325. | ![](media/image298.p | -| png){width="2.9981966316710413in" | ng){width="2.8774507874015747in" | -| height="3.774873140857393in"} | height="2.998788276465442in"} | -+-----------------------------------+----------------------------------+ - -Complete the dialogue as shown in Fig. 19.2c and choose just the 3 -summaries from the sub-dialogue, as shown in Fig. 19.2d. This generates -a new data frame with 30 (years) by 12 (months), i.e. 360 rows of data. -It will be multiples of 360 rows if there is more than one station. - -Return to the dialogue, change the variable, in Fig. 19.2c, to -***raindays*** and omit the ***Maximum*** and also the ***N Non -Missing*** summary -- it isn't needed, because it is just the same as -for the rain column. - - ------------------------------------------------------------------------------------------------------------ - ***Fig. 19.2e The resulting monthly data*** ***Fig. 9.2f*** - ------------------------------------------------------ ----------------------------------------------------- - ![](media/image280.png){width="2.6224245406824145in" ![](media/image294.png){width="3.398500656167979in" - height="3.3829286964129484in"} height="3.334045275590551in"} - - ------------------------------------------------------------------------------------------------------------ - -Check the resulting data frame, shown in Fig. 19.2e. For example, the -first row shows there was a total of 26.4mm from 5 rain days in -1981[^60]. The maximum daily value was 14.4mm in January 1981. In Fig. -19.2e, check there are no missing months. With the setting for missing -values unchecked in Fig. 19.2c, a month will be set to missing if there -is even a single missing day in that month. We consider this issue at -the start of Section 19.3. - -The (World Meteorological Organization (WMO), 2017) describes four -different parameters that can become monthly normals. From the daily -data it may be a mean, or a sum, or a count or an extreme. In Fig. 19.2e -there are 3 of these types. Thus, the rainfall totals are an example of -a sum, the number of rain days is a count, and the maximum rainfall is -an example of an extreme. Once temperature data are considered, there -will also be examples of means. - -The second step is to produce the climate normals from these monthly -data. This uses the "ordinary" summary dialogue in R-Instat, from -***Prepare \> Column: Reshape \> Column Summaries***, Fig 19.2f, rather -than the special climatic summary. This time the only summary needed is -the mean, Fig. 19.2g. - -The results are a new data frame with just 12 rows, giving the monthly -climate normals, Fig. 19.2h. With multiple stations this would be a data -frame with 12 rows for each station. These can now be copied to a table -or presented graphically. With multiple stations this would be in a -facetted graph. - - ------------------------------------------------------------------------------------------------------------ - ***Fig. 19.2g*** ***Fig. 19.2h The climate normals*** - ------------------------------------------------------ ----------------------------------------------------- - ![](media/image282.png){width="2.8663834208223973in" ![](media/image306.png){width="2.805609142607174in" - height="3.124615048118985in"} height="3.1915343394575677in"} - - ------------------------------------------------------------------------------------------------------------ - -Fig. 19.2i gives a simple graph of the mean monthly totals with the data -from Fig. 19.2h as labels. Fig. 19.2j shows the rain days, where the -months have been changed into the more natural seasonal order. - - ------------------------------------------------------------------------------------------------------------ - ***Fig. 19.2i*** ***Fig. 19.2j*** - ----------------------------------------------------- ------------------------------------------------------ - ![](media/image275.png){width="3.008005249343832in" ![](media/image281.png){width="3.0185575240594926in" - height="2.9874726596675414in"} height="2.9944094488188977in"} - - ------------------------------------------------------------------------------------------------------------ - -Secondary parameters for the rainfall, suggested by (World -Meteorological Organization (WMO), 2017) are the extremes, the quintile -boundaries and the number of rain days above defined thresholds. - -The quintile boundaries are the 0%, 20%, 40%, 60%, 80%, 100% points, -where the 0% and 100% are the monthly extremes. Countries are unlikely -to need them all and this is where the US has chosen quartiles, i.e. 25% -and 75% instead of quintiles. - -In R-Instat either can be found from adapting the second stage of the -calculations. If you would like the extremes and quartiles then use -Prepare \> Column: Reshape \> Column Summaries again, Fig. 19.2f, but -just for the sum_rain variable. In the summaries, Fig. 19.2g use the -Minimum and Maximum for the extremes and the Lower and Upper Quartiles -if they are what you wish. - -If you prefer the quintiles (say 20% and 80% points), use the ***More*** -tab, in Fig. 19.2g, to provide further summaries, Fig. 19.2k, where the -0.2 gives the 20% point. Currently only a single value is allowed, so -use the dialogue a second time to add the 80% point. - -Section 4.5 in (World Meteorological Organization (WMO), 2017) proposes -a definition for the quintile boundaries. R, and hence R-Instat, have 9 -alternative methods for the calculation of quantiles (including -therefore quintiles). The default in R is method 7 and this, -fortunately, coincides with the method proposed in (World Meteorological -Organization (WMO), 2017). - -Fig. 19.2l shows the normals for the mean, as in Fig. 19.2i, as a line -plot. It is together with the minimum, 20%, 80% and maximums for the -1981-2010 period. Note that the minimums and maximums are for the -monthly data, i.e. the maximum of the monthly totals. For the rainfall -data it is also useful to have the daily maximums. - - ------------------------------------------------------------------------------------------------------------- - ***Fig. 19.2k*** ***Fig. 19.2l*** - ------------------------------------------------------ ------------------------------------------------------ - ![](media/image279.png){width="2.3519149168853892in" ![](media/image277.png){width="3.1489687226596677in" - height="2.540067804024497in"} height="3.1894805336832897in"} - - ------------------------------------------------------------------------------------------------------------- - -It is important to be clear on the differences between the two maximums. -In January in Fig. 19.2m shows the largest monthly total was 331mm. - - ----------------------------------------------------------------------- - ***Fig. 19.2m*** - ----------------------------------------------------------------------- - ![](media/image260.png){width="5.713489720034995in" - height="3.0282895888013996in"} - - ----------------------------------------------------------------------- - -Also, in January, the maximum daily rainfall in the 30 years was 113mm. - -The quartile or quintile boundaries are calculated from the monthly -summaries, (i.e. the second stage in the calculations). The mean number -of days above different thresholds needs the daily data. - -In ***Climatic \> Prepare \> Transform***, Fig. 19.2a change the -threshold from 0.85mm to 5mm, 10mm, etc and then summarise the resulting -column(s) as described above. - -In practice, decide on the thresholds at the start, and then produce the -summaries together with the 1mm threshold. - -The resulting normals are in Fig. 19.2m for 5mm, 10mm and 25mm. - - ------------------------------------------------------------------------------------------------------------- - ***Fig. 19.2n*** ***Fig. 19.2o*** - ------------------------------------------------------ ------------------------------------------------------ - ![](media/image314.png){width="2.9886920384951883in" ![](media/image304.png){width="2.9118350831146107in" - height="2.7532655293088366in"} height="2.8491032370953633in"} - - ------------------------------------------------------------------------------------------------------------- - -Fig. 19.2n presents the normals of the number of rain days at -Dodoma[^61]. It shows that there was an average of 10 rain days in -January. Of these, just under half were between 1mm and 5mm and there -were about 2 days per month, on average, with more than 25mm. - -So far, we have considered monthly normals for the 1981-2010 rainfall -data. The third stage is to produce annual normals. The (World -Meteorological Organization (WMO), 2017) recommend producing them from -the monthly normals, i.e. from the data in Fig. 19.2m, rather than from -the monthly data, e.g. Fig 19.2e. If there are no missing values the -results are essentially the same. - -From the monthly normals in Fig. 19.2m use ***Prepare \> Column: Reshape -\> Column Summaries*** again, Fig. 19.2o, with the five variables -***meanrain, rainday, rainday5, rainday10*** and ***rainday25***. In -Fig. 19.2o press the ***Summaries*** sub-dialogue and just get the -***Sum***. Also, in Fig. 19.2o, the results could be stored in another -data frame if the calculations were for multiple stations. We choose -here to give the results in the ***output window*** instead, Fig. 19.2p. - -Now return to the dialogue in Fig. 19.2o. Use the variable ***maxrain*** -instead and change the summary to just produce the ***maximum***. - -The annual results, in Fig. 19.2p show the mean annual rainfall was -595mm from 43 rain days, of which, on average 7 days has 25mm or more. -So, the mean rain per rain day was on average 14mm and about one rain -day in six had 25mm or more. The largest ever daily rainfall was 113mm. - -+--------------------------------------+-------------------------------+ -| ***Fig. 19.2p*** | ***Fig. 19.2q*** | -| | | -| | ***Prepare \> Column: Reshape | -| | \> Column Summaries (after | -| | making year a factor)*** | -+======================================+===============================+ -| ![](media/image | ![](media/image293.png | -| 297.png){width="3.388011811023622in" | ){width="2.658290682414698in" | -| height="1.6162992125984252in"} | height="2.639235564304462in"} | -+--------------------------------------+-------------------------------+ - -The (World Meteorological Organization (WMO), 2017) recommendation of -calculating the annual normals from the monthly values does not work for -the quintiles. In the calculations above we have used the nice property -that "the sum of the means is the same as the mean of the sums". So, in -the figures above, totalling the monthly values in Fig. 19.2e to give -the 30 annual values and then taking the mean over the years, still -gives the value of 595mm that we found doing it "the other way round". - -One limitation with this recommendation is that it is not possible to -calculate the annual normal quintiles, i.e. the variables minrain, 20% -(q20) , q80 and maxrain, see Fig. 19.2m, from their monthly -counterparts. The same applies to the quartiles, see Table 19.1b above, -from (Arguez, et al., 2012) where the annual quartiles have been -omitted. - -These quintiles, including the annual extremes, are useful. As there are -no missing values in the data, they are calculated from the individual -monthly values, shown in Fig. 19.2e. - -With the monthly data frame, Fig. 19.2e, right-click in the year name -and make the year into a factor column. Then use ***Prepare \> Column: -Reshape \> Column Summaries*** again as shown in Fig. 19.2q, for the -sumrain variable. - -In the summaries sub-dialogue just get the ***Sum***. The resulting data -frame is shown in Fig. 19.2r. - -Use the ***Prepare \> Column: Reshape \> Column Summaries*** in this new -data frame. With the ***Summaries*** sub-dialogue give the ***Mean, -Minimum,*** ***Maximum*** and the ***0.2 percentile*** (on the More -tab). Use the same dialogue again, and change 0.2 to 0.8 to give the 80% -point. - -The results are in Fig. 19.2s. The first value simply confirms that the -mean is the same, whichever way it is calculated. The lowest year had a -total of 330mm and the highest was 864mm. The 20% point for the annual -rainfall total was 487mm and the 80% point was 717mm. - -+---------------------------+------------------------------------------+ -| ***Fig. 19.2r*** | ***Fig. 19.2s Annual results*** | -| | | -| | ***From Prepare \> Column: Reshape \> | -| | Column Summaries*** | -+===========================+==========================================+ -| ![ | ![](media/im | -| ](media/image307.png){wid | age303.png){width="3.7290562117235346in" | -| th="2.3395986439195102in" | height="1.6612860892388452in"} | -| heig | | -| ht="2.445317147856518in"} | | -+---------------------------+------------------------------------------+ - -## Missing values - -Make a copy of the rainfall column, to illustrate how to cope with -missing values. - -***Right-click*** in the ***rain variable***, Fig. 19.3a and choose -***Duplicate Column***. Call the resulting variable ***rainm***, Fig. -19.3b. - - ------------------------------------------------------------------------------------------------------------- - ***Fig. 19.3a*** ***Fig. 19.3b*** - ------------------------------------------------------ ------------------------------------------------------ - ![](media/image291.png){width="3.0459667541557307in" ![](media/image296.png){width="2.8682020997375326in" - height="3.0348293963254593in"} height="2.8682020997375326in"} - - ------------------------------------------------------------------------------------------------------------- - -In the resulting column, double-click on 7^th^, 8^th^ and 9^th^ January -and make the values into NA. Scroll down and make 1^st^ to 5^th^ -February 1981 into NA. - -Then use Climatic \> Prepare \> Transform, Fig. 19.3c, to make a column -called raindaym. The resulting data are shown in Fig. 19.3d. - - ---------------------------------------------------------------------------------------------------------- - ***Fig. 19.3c*** ***Fig. 19.3d*** - ----------------------------------------------------- ---------------------------------------------------- - ![](media/image310.png){width="2.964792213473316in" ![](media/image289.png){width="2.98044728783902in" - height="4.0111898512685915in"} height="2.9964720034995627in"} - - ---------------------------------------------------------------------------------------------------------- - -The guidelines in (World Meteorological Organization (WMO), 2017) depend -on what type of parameter you are calculating, i.e. sum, mean, count or -extreme. - -+--------------------------------+-------------------------------------+ -| ***Fig. 19.3e*** | ***Fig. 19.3f*** | -| | | -| | ***[Redo when new option | -| | available]{.mark}*** | -+================================+=====================================+ -| ![](media/image593.pn | ![](media/image58 | -| g){width="2.739374453193351in" | 2.png){width="3.2279877515310584in" | -| height="3.505337926509186in"} | height="2.816849300087489in"} | -+--------------------------------+-------------------------------------+ - -It is strict for a sum parameter, so here for the total monthly -rainfall. If there are ***any*** missing values, it proposes the monthly -sum be set to missing. - -This is also one of the default settings in R, and hence in R-Instat. -So, repeat the ***Climatic \> Prepare \> Climatic Summaries*** dialogue, -from Fig. 19.2b, also shown in Fig. 19.3e, for the new ***rainm*** -variable. Just get the ***sum***. - -The maximum daily rainfall is an extreme. When there are missing values -in the month, the extreme is found for those that remain present. So, -return to the ***Prepare \> Column: Reshape \> Column Summaries*** -dialogue, tick the ***Omit Missing Values*** checkbox in the dialogue -shown in Fig. 19.3e. Click the ***Summaries button*** and change the -summary to give just the ***Maximum***. - -When the parameter is a count, like the number of rain days, (or a -mean), there is an intermediate recommendation, shown in Fig. 19.3f. The -monthly summary is set to missing if there are 11 or more missing days -in the month, or if 5, or more, consecutive days are missing[^62]. - - ------------------------------------------------------------------------------------------------------------- - ***Fig. 19.3g*** ***Fig. 19.3h*** - ------------------------------------------------------ ------------------------------------------------------ - ![](media/image581.png){width="2.6387160979877518in" ![](media/image577.png){width="3.3559295713035873in" - height="2.633252405949256in"} height="2.6931856955380575in"} - - ------------------------------------------------------------------------------------------------------------- - -Return to the ***Prepare \> Column: Reshape \> Column Summaries*** -dialogue, Fig. 19.3e, yet again and use the ***raindaym*** variable. -Click on the Summaries and choose ***N Non Missing*** and ***Sum***. On -the main dialogue also tick the Add Date Column[^63] checkbox. - -The results are shown in Fig. 19.3h. With the missing values, the first -2 months in 1981 are set to missing for the rainfall total and neither -month is missing for the maximum. For the number of rain days, the first -month is summarised, because just 3 days were missing. The second has -been set to NA, because 5 consecutive days were missing. - -With missing values (World Meteorological Organization (WMO), 2017) -propose one further adjustment for the count-type normals, that are here -represented by the number of rain days. The first row of data in Fig. -19.3h shows there were 4 rain days in the 28 non-missing days in January -1981. There are 31 days in January and hence the value is multiplied by -31/28, which gives an estimate of 4.4 rain days in the full month. - -To handle this adjustment, use ***Climatic \> Date \> Use Date*** as -shown in Fig. 19.3i. Just choose the check-box for ***Days in Month***. -The resulting column is also shown in Fig. 19.3h. Now use ***Prepare \> -Column: Calculate \> Calculations*** and complete it as shown in Fig. -19.3j. The resulting variable is also shown in Fig. 19.3h. - -+--------------------------------+-------------------------------------+ -| ***Fig. 19.3i Number of days | ***Fig. 19.3j*** | -| in each month*** | | -| | | -| ***Climatic \> Date \> Use | | -| Date*** | | -+================================+=====================================+ -| ![](media/image580.pn | ![](media/image57 | -| g){width="2.790554461942257in" | 8.png){width="3.1834765966754155in" | -| height="2.93128937007874in"} | height="2.9771905074365703in"} | -+--------------------------------+-------------------------------------+ - -The second stage in the calculations is the summary of the normal for -each month, as shown in Section 19.2. The recommendation is that the -monthly normals should only be calculated where there are at least 80%, -i.e. 24 of the 30 years that are not missing. In the example here, there -is missing in only a single year. Hence the second and third stages can -proceed as described in Section 19.2. - -This same rule of needing 80% of the years also applies to the -calculations of the monthly quintiles. The annual quintiles, unlike the -other normal, can not be calculated from the monthly normal. Hence -annual quintiles should not be calculated if there are missing months in -the data. - -## Temperature normals - -In (World Meteorological Organization (WMO), 2017) the monthly (and -annual) mean values of the (daily) Tmax, Tmin and Tmean are in the list -of Principal normals, [[Table 19.1a]{.underline}](#bookmark=id.4anzqyu), -while the monthly extremes and the count of the number of days that Tmax -exceeds 25˚C, 30˚C, 35˚C and 40˚C are listed as secondary. The only -equivalent threshold for Tmin is the count less than 0˚C, which is -rarely useful in Africa. In (Arguez, et al., 2012) the count less than -10˚C is used, see [[Table 19.1b]{.underline}](#bookmark=id.2pta16n) and -that may be more relevant. - -There are missing values in the temperature record. The inventory in -Fig. 19.1a indicated that there are not many missing values, but a more -accurate check may be useful. One way again uses ***Climatic \> Check -Data \> Inventory***, as shown in Fig. 19.4a, but with a different -layout of the data. The result is in Fig. 19.4b. - -+---------------------------+------------------------------------------+ -| ***Fig. 19.4a Detailed | ***Fig. 19.4b Results for Tmax and Tmin | -| inventory*** | 1981-2010*** | -| | | -| ***Climatic \> Check Data | | -| \> Inventory*** | | -+===========================+==========================================+ -| ! | ![](media/im | -| [](media/image576.png){wi | age579.png){width="3.6292169728783903in" | -| dth="2.362328302712161in" | height="3.4070188101487315in"} | -| heig | | -| ht="2.666806649168854in"} | | -+---------------------------+------------------------------------------+ - -This confirms that there are only a few missing values. A more precise -result would be through a table. This is not currently an automatic -option in R-Instat. However, it can easily be given as was shown in -Chapter 8, giving the results in Fig. 19.4c. They show the thin red -lines in Fig. 19.4b refer to isolated single missing days. There are -just 2 years with at least a missing month for Tmax and one year for -Tmin. The analysis can continue. - - ----------------------------------------------------------------------- - ***Fig. 19.4c Count of missing values in Tmax, Dodoma 1981-2010*** - ----------------------------------------------------------------------- - ![](media/image569.png){width="6.268055555555556in" height="4.25625in"} - - ----------------------------------------------------------------------- - -Tmin is used for illustration. The main dialogue is ***Climatic \> -Prepare \> Climatic Summaries***, Fig. 19.4d. - - ------------------------------------------------------------------------------------------------------------ - ***Fig. 19.4d*** ***Fig. 19.4e*** - ------------------------------------------------------ ----------------------------------------------------- - ![](media/image588.png){width="2.9493580489938758in" ![](media/image596.png){width="2.993937007874016in" - height="3.6728904199475068in"} height="3.0913003062117235in"} - - ------------------------------------------------------------------------------------------------------------ - - ------------------------------------------------------------------------------------------------------------ - ***Fig. 19.4f*** ***Fig. 19.4g*** - ------------------------------------------------------ ----------------------------------------------------- - ![](media/image587.png){width="2.798834208223972in" ![](media/image613.png){width="3.347797462817148in" - height="1.2322878390201224in"} height="2.8662959317585304in"} - - ![](media/image598.png){width="2.7431364829396325in" - height="1.68996719160105in"} - ------------------------------------------------------------------------------------------------------------ - -The results are shown in Fig. 19.4g. For example, in July 1984 the -minimum of Tmin was 12.3˚C, the mean was 14.0˚C and the maximum was 15.8 -˚C. These were from 30 days, because one day was missing. 25 out of the -30 days were less than 15 ˚C. This count is adjusted as described in -Fig. 19.3i, i.e. use Climatic \> Dates \> Use Date to add a variable -giving the number of days in each month and then adjust the count of -days less than 15 ˚C by: - -Countlt15/count_non_missing \* days_in month. - -This gives the last variable shown in Fig. 19.4g. - -The second stage is to average over the years. This uses ***Prepare \> -Column: Reshape \> Column Summaries*** as for the rainfall normals, Fig. -19.4h. - - ------------------------------------------------------------------------------------------------------------ - ***Fig. 19.4h*** ***Fig. 19.4i*** - ----------------------------------------------------- ------------------------------------------------------ - ![](media/image601.png){width="2.648307086614173in" ![](media/image594.png){width="3.4425153105861765in" - height="2.638747812773403in"} height="2.5276388888888888in"} - - ------------------------------------------------------------------------------------------------------------ - - ------------------------------------------------------------------------------------------------------------ - ***Fig. 19.4j*** ***Fig. 19.4k*** - ------------------------------------------------------ ----------------------------------------------------- - ![](media/image586.png){width="3.2818733595800524in" ![](media/image590.png){width="2.493397856517935in" - height="3.1984864391951007in"} height="3.3734208223972004in"} - +# Climate Normals +## Introduction + +The calculation of climate normals in this chapter is based largely on +(World Meteorological Organization (WMO), 2017). We also consider the +adaptation of the guidelines to the calculations of the normals in the +US, as described in (Arguez, et al., 2012). + +A climatological standard normal now refers to the most recent 30-year +period finishing in a zero, i.e. currently 1981-2010, and soon to be +1991-2020. In addition, the 1961-1990 period is retained as a standard +reference period for assessing long-term climate change. + +A distinction is made in (World Meteorological Organization (WMO), +2017), between "Principal Climatological Parameters" and "Secondary +Parameters". There are 8 primary parameters including monthly total +rainfall (precipitation) and the total number of rain days, Table 19.1a. + + ----------------------------------------------------------------------- + ***Table 19.1a WMO Principal Climatological + Parameters*** + ------------------------------------------------------- --------------- + **Parameter** **Units** + + Precipitation total mm + + Precipitation days (Precip ≥ 1mm) days + + Mean Tmax °C + + Mean Tmin °C + + Mean Tavg °C + + Mean sea-level pressure hPa + + Mean vapour pressure hPa + + Total hours of sunshine hours + ----------------------------------------------------------------------- + +The quintile boundaries for rainfall (mm) and the mean number of days +with more than 5, 10, 50, 100 and 150mm are secondary parameters. +Temperature thresholds and extremes are also included. + +These are intended as guidelines and are adapted by individual +countries. Examples from the US are shown in Table 19.1b. This table is +adapted from Table 5 in (Arguez, et al., 2012). The units have been +changed to millimetres for rainfall and °C for temperatures (US uses +inches and Fahrenheit.) + + -------------------------------------------------------------------------------------------------------- + Table 19.1b + Monthly and + annual + normals for + a station in + Chicago, + from + (Arguez, et + al., 2012) + ------------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------- + Variable J F M A M J J A S O N D Ann + + Tmax (°C) -0.3 2.1 8.2 15.1 21.2 26.6 29.0 27.8 24.1 17.1 9.2 1.8 15.2 + + Tavg (°C) -4.0 -1.8 3.8 10.2 16.1 21.7 24.4 23.4 19.1 12.3 5.3 -1.7 10.8 + + Tmin (°C) -7.7 -5.7 -0.6 5.4 10.9 16.7 19.7 19.0 14.2 7.6 1.4 -5.2 6.4 + + DTR (°C) 7.4 7.8 8.8 9.7 10.3 9.9 9.3 8.8 9.9 9.5 7.8 7.0 8.8 + + Precip(mm) 52 49 69 92 105 103 102 101 84 82 87 65 993 + + HDD 692 564 451 249 104 17 1 2 43 194 391 620 3327 + + CDD 0 0 1 7 34 117 188 160 66 9 0 0 581 + + Days Tmax \> 0 0 0 0 0.6 3.1 6.3 3.8 1.2 0 0 0 15.1 + 32.2 + + Days with 1.4 2.9 10.6 23.5 30.5 30 31 31 30 28.1 13.1 2.9 235 + Tmin \< 10 + + Precip 25% 29 26 41 54 63 70 53 57 40 49 48 38 + + Precip 75% 75 66 90 119 141 124 115 143 117 93 133 80 + + Precip \> 10.7 8.8 11.2 11.1 11.4 10.3 9.9 9 8.2 10.2 11.2 11.1 123.1 + 0.2mm[^59] + + Precip \> 0.2 0.2 0.3 0.9 1 1.3 1 1.3 0.7 0.8 0.8 0.5 9 + 25mm + -------------------------------------------------------------------------------------------------------- + +One differences is for rainfall, where WMO suggests quintiles, i.e. 20%, +to 80%, while the US uses quartiles (25% and 75%). Heating (HDD) and +cooling degree days are also including. A heating degree day is defined +as a value of Tavg above 18°C (65 degrees Fahrenheit), while CDDs are +temperatures below that level. + +The WMO lower threshold for rainfall is proposed as ≥ 1mm. We have +largely used 0.85mm as a practical lower limit in this guide. We claim +this is consistent with the WMO value of ≥1mm. For practical purposes, +as data are recorded to 0.1mm the WMO value is effectively \> 0.95mm. +For consistency between stations (which is important for climate +normals) the value of 0.85mm is about the same. But it allows for +differences in rounding at different stations. This can occur in 2 ways. +If data were originally in inches, then 0.01inch = 0.3mm. The value of +0.9mm is not possible, because 0.03inches = 0.8mm, while 0.04inches = +1mm. + +In addition, some observers round data more than others. An observer who +rounds 0.9mm to 1mm would have that day counted as rain, while the more +precise observer, recording the same value as 0.9mm would have it +omitted as dry. + +For these reasons, we claim the proposed threshold value of 0.85mm is a +practical was of implementing the WMO ≥1mm threshold. + + ----------------------------------------------------------------------------------------------------------- + ***Fig. 19.1a Inventory for Dodoma*** ***Fig. 19.1b Subset with 30 years*** + ----------------------------------------------------- ----------------------------------------------------- + ![](figures/Fig19.1a.png){width="2.9576673228346455in" ![](figures/Fig19.1b.png){width="2.8694127296587926in" + height="2.9941371391076115in"} height="3.0189227909011374in"} + + ----------------------------------------------------------------------------------------------------------- + +In principle, producing normals is straightforward as is shown in +Section 19.2 with examples using rainfall data. Complications relate +largely to the presence of missing values in the reference period and +this is discussed in Section 19.3. + +The Dodoma data are used as an example. ***File \> Open from Library \> +Instat \> Browse \> Climatic \> Tanzania \> Dodoma.rds***. + +The data are already defined as climatic. An inventory is shown in Fig. +19.1a. IT shows there are virtually no missing values in the rainfall, +either in the 30 years from 1961 or in the most recent period, from 1981 +to2010. A subset of the data is produced as shown in Fig. 19.1b, and +rainfall normals from 1981-2010 are shown in Section 19.2. + +There are also relatively few missing values in the temperatures. They +are considered in Section 19.3, where we also explain the WMO +recommendations for coping with missing values. + +The sunshine records only started in 1973, and so could not be used for +1961-90 normals. And there are far too many missing values for them to +be used in 1981-2010, unless they can be merged with satellite data. +This is considered in Section 19.4. + +The examples here are for a single station. Usually they would be done +for a whole set of stations in a single file, and that is no more work. +The process, in R-Instat, currently involves three successive steps. +There seems to be no R-package for this task. We expect to construct one +for R and hence R-Instat, in the future. + +## Precipitation normals + +From Fig. 19.1b the Dodoma data are now from 1981 to 2010. We have +chosen to keep the year from January to December, though there could be +a case for July to June, as that would mean each "year" would be a +complete season. The rains in Dodoma are from November to April. In +(World Meteorological Organization (WMO), 2017), mention is made of +climate normals being for seasons rather than annual, but no details are +given, In Tanzania part of the country is unimodal and part is bimodal, +so comparisons of the normals between stations would be easier with a +consistent definition and January to December therefore seems justified. + +The first 2 normals in Table 19.1a are the precipitation totals and the +number of rain days. As preparation, calculate the rain days as shown in +Fig. 19.2a. In Fig. 19.2a the 0.85mm threshold has been used, which we +claimed above, is consistent with the WMO definition of rain ≥ 1mm. (Use +0.95mm is you don't agree!) + + ----------------------------------------------------------------------------------------------------------- + ***Fig. 19.2a Add a variable for rain days*** ***Fig. 19.2b*** + ----------------------------------------------------- ----------------------------------------------------- + ![](figures/Fig19.2a.png){width="2.7958967629046367in" ![](figures/Fig19.2b.png){width="3.2288713910761153in" + height="3.432683727034121in"} height="3.409433508311461in"} + + ----------------------------------------------------------------------------------------------------------- + +The resulting daily data are in Fig. 19.2b. The rainday variable can be +seen to be 1 on rain days, and 0 otherwise. + +Getting the monthly normals is a 2-step process and the annual normals +adds a 3rd step. + +The first step uses the ***Climatic \> Prepare \> Climatic Summaries***, +as shown in Fig. 19.2c, to give the monthly rainfall totals for each +year. + + ----------------------------------------------------------------------------------------------------------- + ***Fig. 19.2c*** ***Fig. 19.2d*** + ----------------------------------------------------- ----------------------------------------------------- + ![](figures/Fig19.2c.png){width="2.9981966316710413in" ![](figures/Fig19.2d.png){width="2.8774507874015747in" + height="3.774873140857393in"} height="2.998788276465442in"} + + ----------------------------------------------------------------------------------------------------------- + +Complete the dialogue as shown in Fig. 19.2c and choose just the 3 +summaries from the sub-dialogue, as shown in Fig. 19.2d. This generates +a new data frame with 30 (years) by 12 (months), i.e. 360 rows of data. +It will be multiples of 360 rows if there is more than one station. + +Return to the dialogue, change the variable, in Fig. 19.2c, to +***raindays*** and omit the ***Maximum*** and also the ***N Non +Missing*** summary -- it isn't needed, because it is just the same as +for the rain column. + + ------------------------------------------------------------------------------------------------------------ + ***Fig. 19.2e The resulting monthly data*** ***Fig. 9.2f*** + ------------------------------------------------------ ----------------------------------------------------- + ![](figures/Fig19.2e.png){width="2.6224245406824145in" ![](figures/Fig19.2f.png){width="3.398500656167979in" + height="3.3829286964129484in"} height="3.334045275590551in"} + + ------------------------------------------------------------------------------------------------------------ + +Check the resulting data frame, shown in Fig. 19.2e. For example, the +first row shows there was a total of 26.4mm from 5 rain days in +1981[^60]. The maximum daily value was 14.4mm in January 1981. In Fig. +19.2e, check there are no missing months. With the setting for missing +values unchecked in Fig. 19.2c, a month will be set to missing if there +is even a single missing day in that month. We consider this issue at +the start of Section 19.3. + +The (World Meteorological Organization (WMO), 2017) describes four +different parameters that can become monthly normals. From the daily +data it may be a mean, or a sum, or a count or an extreme. In Fig. 19.2e +there are 3 of these types. Thus, the rainfall totals are an example of +a sum, the number of rain days is a count, and the maximum rainfall is +an example of an extreme. Once temperature data are considered, there +will also be examples of means. + +The second step is to produce the climate normals from these monthly +data. This uses the "ordinary" summary dialogue in R-Instat, from +***Prepare \> Column: Reshape \> Column Summaries***, Fig 19.2f, rather +than the special climatic summary. This time the only summary needed is +the mean, Fig. 19.2g. + +The results are a new data frame with just 12 rows, giving the monthly +climate normals, Fig. 19.2h. With multiple stations this would be a data +frame with 12 rows for each station. These can now be copied to a table +or presented graphically. With multiple stations this would be in a +facetted graph. + + ------------------------------------------------------------------------------------------------------------ + ***Fig. 19.2g*** ***Fig. 19.2h The climate normals*** + ------------------------------------------------------ ----------------------------------------------------- + ![](figures/Fig19.2g.png){width="2.8663834208223973in" ![](figures/Fig19.2h.png){width="2.805609142607174in" + height="3.124615048118985in"} height="3.1915343394575677in"} + + ------------------------------------------------------------------------------------------------------------ + +Fig. 19.2i gives a simple graph of the mean monthly totals with the data +from Fig. 19.2h as labels. Fig. 19.2j shows the rain days, where the +months have been changed into the more natural seasonal order. + + ------------------------------------------------------------------------------------------------------------ + ***Fig. 19.2i*** ***Fig. 19.2j*** + ----------------------------------------------------- ------------------------------------------------------ + ![](figures/Fig19.2i.png){width="3.008005249343832in" ![](figures/Fig19.2j.png){width="3.0185575240594926in" + height="2.9874726596675414in"} height="2.9944094488188977in"} + + ------------------------------------------------------------------------------------------------------------ + +Secondary parameters for the rainfall, suggested by (World +Meteorological Organization (WMO), 2017) are the extremes, the quintile +boundaries and the number of rain days above defined thresholds. + +The quintile boundaries are the 0%, 20%, 40%, 60%, 80%, 100% points, +where the 0% and 100% are the monthly extremes. Countries are unlikely +to need them all and this is where the US has chosen quartiles, i.e. 25% +and 75% instead of quintiles. + +In R-Instat either can be found from adapting the second stage of the +calculations. If you would like the extremes and quartiles then use +Prepare \> Column: Reshape \> Column Summaries again, Fig. 19.2f, but +just for the sum_rain variable. In the summaries, Fig. 19.2g use the +Minimum and Maximum for the extremes and the Lower and Upper Quartiles +if they are what you wish. + +If you prefer the quintiles (say 20% and 80% points), use the ***More*** +tab, in Fig. 19.2g, to provide further summaries, Fig. 19.2k, where the +0.2 gives the 20% point. Currently only a single value is allowed, so +use the dialogue a second time to add the 80% point. + +Section 4.5 in (World Meteorological Organization (WMO), 2017) proposes +a definition for the quintile boundaries. R, and hence R-Instat, have 9 +alternative methods for the calculation of quantiles (including +therefore quintiles). The default in R is method 7 and this, +fortunately, coincides with the method proposed in (World Meteorological +Organization (WMO), 2017). + +Fig. 19.2l shows the normals for the mean, as in Fig. 19.2i, as a line +plot. It is together with the minimum, 20%, 80% and maximums for the +1981-2010 period. Note that the minimums and maximums are for the +monthly data, i.e. the maximum of the monthly totals. For the rainfall +data it is also useful to have the daily maximums. + + ------------------------------------------------------------------------------------------------------------- + ***Fig. 19.2k*** ***Fig. 19.2l*** + ------------------------------------------------------ ------------------------------------------------------ + ![](figures/Fig19.2k.png){width="2.3519149168853892in" ![](figures/Fig19.2l.png){width="3.1489687226596677in" + height="2.540067804024497in"} height="3.1894805336832897in"} + + ------------------------------------------------------------------------------------------------------------- + +It is important to be clear on the differences between the two maximums. +In January in Fig. 19.2m shows the largest monthly total was 331mm. + + ----------------------------------------------------------------------- + ***Fig. 19.2m*** + ----------------------------------------------------------------------- + ![](figures/Fig19.2m.png){width="5.713489720034995in" + height="3.0282895888013996in"} + + ----------------------------------------------------------------------- + +Also, in January, the maximum daily rainfall in the 30 years was 113mm. + +The quartile or quintile boundaries are calculated from the monthly +summaries, (i.e. the second stage in the calculations). The mean number +of days above different thresholds needs the daily data. + +In ***Climatic \> Prepare \> Transform***, Fig. 19.2a change the +threshold from 0.85mm to 5mm, 10mm, etc and then summarise the resulting +column(s) as described above. + +In practice, decide on the thresholds at the start, and then produce the +summaries together with the 1mm threshold. + +The resulting normals are in Fig. 19.2m for 5mm, 10mm and 25mm. + + ------------------------------------------------------------------------------------------------------------- + ***Fig. 19.2n*** ***Fig. 19.2o*** + ------------------------------------------------------ ------------------------------------------------------ + ![](figures/Fig19.2n.png){width="2.9886920384951883in" ![](figures/Fig19.2o.png){width="2.9118350831146107in" + height="2.7532655293088366in"} height="2.8491032370953633in"} + + ------------------------------------------------------------------------------------------------------------- + +Fig. 19.2n presents the normals of the number of rain days at +Dodoma[^61]. It shows that there was an average of 10 rain days in +January. Of these, just under half were between 1mm and 5mm and there +were about 2 days per month, on average, with more than 25mm. + +So far, we have considered monthly normals for the 1981-2010 rainfall +data. The third stage is to produce annual normals. The (World +Meteorological Organization (WMO), 2017) recommend producing them from +the monthly normals, i.e. from the data in Fig. 19.2m, rather than from +the monthly data, e.g. Fig 19.2e. If there are no missing values the +results are essentially the same. + +From the monthly normals in Fig. 19.2m use ***Prepare \> Column: Reshape +\> Column Summaries*** again, Fig. 19.2o, with the five variables +***meanrain, rainday, rainday5, rainday10*** and ***rainday25***. In +Fig. 19.2o press the ***Summaries*** sub-dialogue and just get the +***Sum***. Also, in Fig. 19.2o, the results could be stored in another +data frame if the calculations were for multiple stations. We choose +here to give the results in the ***output window*** instead, Fig. 19.2p. + +Now return to the dialogue in Fig. 19.2o. Use the variable ***maxrain*** +instead and change the summary to just produce the ***maximum***. + +The annual results, in Fig. 19.2p show the mean annual rainfall was +595mm from 43 rain days, of which, on average 7 days has 25mm or more. +So, the mean rain per rain day was on average 14mm and about one rain +day in six had 25mm or more. The largest ever daily rainfall was 113mm. + + ------------------------------------------------------------------------------------------------------------- + ***Fig. 19.2p*** ***Fig. 19.2q*** + ------------------------------------------------------ ------------------------------------------------------ + ![](figures/Fig19.2p.png){width="3.388011811023622in" ![](figures/Fig19.2q.png){width="2.658290682414698in" + height="1.6162992125984252in"} height="2.639235564304462in"} + + ------------------------------------------------------------------------------------------------------------- + +The (World Meteorological Organization (WMO), 2017) recommendation of +calculating the annual normals from the monthly values does not work for +the quintiles. In the calculations above we have used the nice property +that "the sum of the means is the same as the mean of the sums". So, in +the figures above, totalling the monthly values in Fig. 19.2e to give +the 30 annual values and then taking the mean over the years, still +gives the value of 595mm that we found doing it "the other way round". + +One limitation with this recommendation is that it is not possible to +calculate the annual normal quintiles, i.e. the variables minrain, 20% +(q20) , q80 and maxrain, see Fig. 19.2m, from their monthly +counterparts. The same applies to the quartiles, see Table 19.1b above, +from (Arguez, et al., 2012) where the annual quartiles have been +omitted. + +These quintiles, including the annual extremes, are useful. As there are +no missing values in the data, they are calculated from the individual +monthly values, shown in Fig. 19.2e. + +With the monthly data frame, Fig. 19.2e, right-click in the year name +and make the year into a factor column. Then use ***Prepare \> Column: +Reshape \> Column Summaries*** again as shown in Fig. 19.2q, for the +sumrain variable. + +In the summaries sub-dialogue just get the ***Sum***. The resulting data +frame is shown in Fig. 19.2r. + +Use the ***Prepare \> Column: Reshape \> Column Summaries*** in this new +data frame. With the ***Summaries*** sub-dialogue give the ***Mean, +Minimum,*** ***Maximum*** and the ***0.2 percentile*** (on the More +tab). Use the same dialogue again, and change 0.2 to 0.8 to give the 80% +point. + +The results are in Fig. 19.2s. The first value simply confirms that the +mean is the same, whichever way it is calculated. The lowest year had a +total of 330mm and the highest was 864mm. The 20% point for the annual +rainfall total was 487mm and the 80% point was 717mm. + + ------------------------------------------------------------------------------------------------------------- + ***Fig. 19.2r*** ***Fig. 19.2s Annual results*** + ------------------------------------------------------ ------------------------------------------------------ + ![](figures/Fig19.2r.png){width="2.3395986439195102in" ![](figures/Fig19.2s.png){width="3.7290562117235346in" + height="2.445317147856518in"} height="1.6612860892388452in"} + + ------------------------------------------------------------------------------------------------------------- + +## Missing values + +Make a copy of the rainfall column, to illustrate how to cope with +missing values. + +***Right-click*** in the ***rain variable***, Fig. 19.3a and choose +***Duplicate Column***. Call the resulting variable ***rainm***, Fig. +19.3b. + + ------------------------------------------------------------------------------------------------------------- + ***Fig. 19.3a*** ***Fig. 19.3b*** + ------------------------------------------------------ ------------------------------------------------------ + ![](figures/Fig19.3a.png){width="3.0459667541557307in" ![](figures/Fig19.3b.png){width="2.8682020997375326in" + height="3.0348293963254593in"} height="2.8682020997375326in"} + + ------------------------------------------------------------------------------------------------------------- + +In the resulting column, double-click on 7^th^, 8^th^ and 9^th^ January +and make the values into NA. Scroll down and make 1^st^ to 5^th^ +February 1981 into NA. + +Then use Climatic \> Prepare \> Transform, Fig. 19.3c, to make a column +called raindaym. The resulting data are shown in Fig. 19.3d. + + ---------------------------------------------------------------------------------------------------------- + ***Fig. 19.3c*** ***Fig. 19.3d*** + ----------------------------------------------------- ---------------------------------------------------- + ![](figures/Fig19.3c.png){width="2.964792213473316in" ![](figures/Fig19.3d.png){width="2.98044728783902in" + height="4.0111898512685915in"} height="2.9964720034995627in"} + + ---------------------------------------------------------------------------------------------------------- + +The guidelines in (World Meteorological Organization (WMO), 2017) depend +on what type of parameter you are calculating, i.e. sum, mean, count or +extreme. + + ---------------------------------------------------------------------------------------------------------- + ***Fig. 19.3e*** ***Fig. 19.3f*** + ----------------------------------------------------- ---------------------------------------------------- + ![](figures/Fig19.3e.png){width="2.739374453193351in" ![](figures/Fig19.3f.png){width="3.2279877515310584in" + height="3.505337926509186in"} height="2.816849300087489in"} + + ---------------------------------------------------------------------------------------------------------- + +It is strict for a sum parameter, so here for the total monthly +rainfall. If there are ***any*** missing values, it proposes the monthly +sum be set to missing. + +This is also one of the default settings in R, and hence in R-Instat. +So, repeat the ***Climatic \> Prepare \> Climatic Summaries*** dialogue, +from Fig. 19.2b, also shown in Fig. 19.3e, for the new ***rainm*** +variable. Just get the ***sum***. + +The maximum daily rainfall is an extreme. When there are missing values +in the month, the extreme is found for those that remain present. So, +return to the ***Prepare \> Column: Reshape \> Column Summaries*** +dialogue, tick the ***Omit Missing Values*** checkbox in the dialogue +shown in Fig. 19.3e. Click the ***Summaries button*** and change the +summary to give just the ***Maximum***. + +When the parameter is a count, like the number of rain days, (or a +mean), there is an intermediate recommendation, shown in Fig. 19.3f. The +monthly summary is set to missing if there are 11 or more missing days +in the month, or if 5, or more, consecutive days are missing[^62]. + + ------------------------------------------------------------------------------------------------------------- + ***Fig. 19.3g*** ***Fig. 19.3h*** + ------------------------------------------------------ ------------------------------------------------------ + ![](figures/Fig19.3g.png){width="2.6387160979877518in" ![](figures/Fig19.3h.png){width="3.3559295713035873in" + height="2.633252405949256in"} height="2.6931856955380575in"} + + ------------------------------------------------------------------------------------------------------------- + +Return to the ***Prepare \> Column: Reshape \> Column Summaries*** +dialogue, Fig. 19.3e, yet again and use the ***raindaym*** variable. +Click on the Summaries and choose ***N Non Missing*** and ***Sum***. On +the main dialogue also tick the Add Date Column[^63] checkbox. + +The results are shown in Fig. 19.3h. With the missing values, the first +2 months in 1981 are set to missing for the rainfall total and neither +month is missing for the maximum. For the number of rain days, the first +month is summarised, because just 3 days were missing. The second has +been set to NA, because 5 consecutive days were missing. + +With missing values (World Meteorological Organization (WMO), 2017) +propose one further adjustment for the count-type normals, that are here +represented by the number of rain days. The first row of data in Fig. +19.3h shows there were 4 rain days in the 28 non-missing days in January +1981. There are 31 days in January and hence the value is multiplied by +31/28, which gives an estimate of 4.4 rain days in the full month. + +To handle this adjustment, use ***Climatic \> Date \> Use Date*** as +shown in Fig. 19.3i. Just choose the check-box for ***Days in Month***. +The resulting column is also shown in Fig. 19.3h. Now use ***Prepare \> +Column: Calculate \> Calculations*** and complete it as shown in Fig. +19.3j. The resulting variable is also shown in Fig. 19.3h. + + ------------------------------------------------------------------------------------------------------------- + ***Fig. 19.3i Number of days in each month*** ***Fig. 19.3j*** + ------------------------------------------------------ ------------------------------------------------------ + ![](figures/Fig19.3i.png){width="2.790554461942257in" ![](figures/Fig19.3j.png){width="3.1834765966754155in" + height="2.93128937007874in"} height="2.9771905074365703in"} + + ------------------------------------------------------------------------------------------------------------- + +The second stage in the calculations is the summary of the normal for +each month, as shown in Section 19.2. The recommendation is that the +monthly normals should only be calculated where there are at least 80%, +i.e. 24 of the 30 years that are not missing. In the example here, there +is missing in only a single year. Hence the second and third stages can +proceed as described in Section 19.2. + +This same rule of needing 80% of the years also applies to the +calculations of the monthly quintiles. The annual quintiles, unlike the +other normal, can not be calculated from the monthly normal. Hence +annual quintiles should not be calculated if there are missing months in +the data. + +## Temperature normals + +In (World Meteorological Organization (WMO), 2017) the monthly (and +annual) mean values of the (daily) Tmax, Tmin and Tmean are in the list +of Principal normals, [[Table 19.1a]{.underline}](#bookmark=id.4anzqyu), +while the monthly extremes and the count of the number of days that Tmax +exceeds 25˚C, 30˚C, 35˚C and 40˚C are listed as secondary. The only +equivalent threshold for Tmin is the count less than 0˚C, which is +rarely useful in Africa. In (Arguez, et al., 2012) the count less than +10˚C is used, see [[Table 19.1b]{.underline}](#bookmark=id.2pta16n) and +that may be more relevant. + +There are missing values in the temperature record. The inventory in +Fig. 19.1a indicated that there are not many missing values, but a more +accurate check may be useful. One way again uses ***Climatic \> Check +Data \> Inventory***, as shown in Fig. 19.4a, but with a different +layout of the data. The result is in Fig. 19.4b. + + ------------------------------------------------------------------------------------------------------------- + ***Fig. 19.4a Detailed inventory*** ***Fig. 19.4b Results for Tmax and Tmin 1981-2010*** + ------------------------------------------------------ ------------------------------------------------------ + ![](figures/Fig19.4a.png){width="2.362328302712161in" ![](figures/Fig19.4b.png){width="3.6292169728783903in" + height="2.666806649168854in"} height="3.4070188101487315in"} + + ------------------------------------------------------------------------------------------------------------- + +This confirms that there are only a few missing values. A more precise +result would be through a table. This is not currently an automatic +option in R-Instat. However, it can easily be given as was shown in +Chapter 8, giving the results in Fig. 19.4c. They show the thin red +lines in Fig. 19.4b refer to isolated single missing days. There are +just 2 years with at least a missing month for Tmax and one year for +Tmin. The analysis can continue. + + ----------------------------------------------------------------------- + ***Fig. 19.4c Count of missing values in Tmax, Dodoma 1981-2010*** + ----------------------------------------------------------------------- + ![](figures/Fig19.4c.png){width="6.268055555555556in" + height="4.25625in"} + + ----------------------------------------------------------------------- + +Tmin is used for illustration. The main dialogue is ***Climatic \> +Prepare \> Climatic Summaries***, Fig. 19.4d. + + ------------------------------------------------------------------------------------------------------------ + ***Fig. 19.4d*** ***Fig. 19.4e*** + ------------------------------------------------------ ----------------------------------------------------- + ![](figures/Fig19.4d.png){width="2.9493580489938758in" ![](figures/Fig19.4e.png){width="2.993937007874016in" + height="3.6728904199475068in"} height="3.0913003062117235in"} + + ------------------------------------------------------------------------------------------------------------ + + ------------------------------------------------------------------------------------------------------------ + ***Fig. 19.4f*** ***Fig. 19.4g*** + ------------------------------------------------------ ----------------------------------------------------- + ![](figures/Fig19.4f.png){width="2.798834208223972in" ![](figures/Fig19.4g.png){width="3.347797462817148in" + height="1.2322878390201224in"} height="2.8662959317585304in"} + + ------------------------------------------------------------------------------------------------------------ + +The results are shown in Fig. 19.4g. For example, in July 1984 the +minimum of Tmin was 12.3˚C, the mean was 14.0˚C and the maximum was 15.8 +˚C. These were from 30 days, because one day was missing. 25 out of the +30 days were less than 15 ˚C. This count is adjusted as described in +Fig. 19.3i, i.e. use Climatic \> Dates \> Use Date to add a variable +giving the number of days in each month and then adjust the count of +days less than 15 ˚C by: + +Countlt15/count_non_missing \* days_in month. + +This gives the last variable shown in Fig. 19.4g. + +The second stage is to average over the years. This uses ***Prepare \> +Column: Reshape \> Column Summaries*** as for the rainfall normals, Fig. +19.4h. + + ------------------------------------------------------------------------------------------------------------ + ***Fig. 19.4h*** ***Fig. 19.4i*** + ----------------------------------------------------- ------------------------------------------------------ + ![](figures/Fig19.4h.png){width="2.648307086614173in" ![](figures/Fig19.4i.png){width="3.4425153105861765in" + height="2.638747812773403in"} height="2.5276388888888888in"} + + ------------------------------------------------------------------------------------------------------------ + + ------------------------------------------------------------------------------------------------------------ + ***Fig. 19.4j*** ***Fig. 19.4k*** + ------------------------------------------------------ ----------------------------------------------------- + ![](figures/Fig19.4j.png){width="3.2818733595800524in" ![](figures/Fig19.4k.png){width="2.493397856517935in" + height="3.1984864391951007in"} height="3.3734208223972004in"} + ------------------------------------------------------------------------------------------------------------ \ No newline at end of file