Chapter_20_Climate_Normals.qmd

# 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"}

  ------------------------------------------------------------------------------------------------------------