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Chapter_14_The_Seasonal_forecast.qmd
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# The Seasonal forecast
## Introduction
Many countries produce a seasonal forecast. (Hansen, Mason, Sun, & Tall,
2011) provides a review for Sub-Saharan Africa. The forecast, for a
given season, often results from a Regional Climate Outlook Forum
(RCOF), updated and down-scaled by the National Meteorological Service
(NMS). In some countries the forecast is a mixture of results from the
global climate models (GCMs) and statistical methods relating historical
climatic data to sea-surface temperatures. Fig. 13.1a and Fig. 13.1b
give examples of the forecast from Ghana and the Caribbean.
-----------------------------------------------------------------------------------------------------------
***Fig 13.1a Ghana rainfall forecast, April - June ***Fig. 13.1b Caribbean rainfall forecast April --
2015*** June 2015***
----------------------------------------------------- -----------------------------------------------------
{width="2.991641513560805in" {width="3.008535651793526in"
height="3.068241469816273in"} height="2.7479418197725285in"}
-----------------------------------------------------------------------------------------------------------
When statistical methods are used, the Climate Predictability Tool (CPT)
software is usually used to produce the forecast. CPT uses multiple
regression with usually the rainfall as the y (dependent or predictand)
variables and SSTs as the x's (independent, or predictor) variables.
There are usually many x (SST) variables and hence CPT offers the option
of doing a principal component analysis first.
When there are also many y (rainfall) variables, a canonical correlation
analysis may precede the multiple regression analysis.
R-Instat can export data for CPT. Hence one use of R-Instat is to
prepare the y-variables (rainfall or temperature) for analysis with CPT.
Traditionally these are 3-month rainfall totals, but any other summary
is possible, for example 3-month total rain days, or the date of the
start of the rains. The requirement is that there is one summary per
year (per station) and the ***Climatic \> Prepare*** menu provides many
options. This is considered in Section 13.2.
The rainfall (or temperature data) are often station values, but they
may also originate from other sources, e.g. reanalysis, or satellite or
merged data. These are sometimes provided ready for CPT. Sometimes
R-Instat could examine these data also and then prepare a subset for
CPT. This option is considered in Section 13.3
## The Y variables - Examining the rainfall data
One use we propose for R-Instat is to examine the rainfall data, before
it is analysed with CPT. The first example is data from Ghana, already
prepared for CPT. The data are in the R-Instat library, hence use
***File \> Open from Library \> Instat \> Browse \> Climatic \> Ghana***
and open the file called ***rr-amj-1981-2014.txt***. The data are shown
in Fig. 13.2a.
The first 2 lines are the locations (Lat and Long) of each station. Then
there are the rainfall data, the 3-month totals from April to June, for
the 34 years from 1981 to 2014. They are from the 22 synoptic stations
in Ghana.
We also need the locations of the station, but in a separate data frame.
Return to the last dialogue and read the data again. This time read just
the first 2 rows, Fig. 13.2b and give the file a new name.
---------------------------------------------------------------------------------------------------------
***Fig. 13.2a*** ***Fig. 13.2b***
----------------------------------------------------- ---------------------------------------------------
{width="2.998064304461942in" {width="3.0224343832021in"
height="2.7682305336832895in"} height="3.2848982939632547in"}
---------------------------------------------------------------------------------------------------------
The station data are now still the "wrong way round". There is a
dialogue to transpose, but it is simpler to use ***Prepare \> Column:
Reshape \> Stack***, Fig. 13.2c, as shown in Fig. 13.2d.
In Fig. 13.2d put all the columns, except the first to be stacked and
put the STN column to be "carried".
------------------------------------------------------------------------------------------------------------
***Fig. 13.2c*** ***Fig. 13.2d***
------------------------------------------------------ -----------------------------------------------------
{width="3.5934798775153105in" {width="2.477023184601925in"
height="1.7293897637795275in"} height="2.1099081364829395in"}
------------------------------------------------------------------------------------------------------------
In the stacked data the column called STN now has the Lat and Long. Now,
Fig. 13.2e, use the ***Prepare \> Column: Reshape \> Unstack***, as
shown to produce the location data as shown in Fig. 13.2f.
-------------------------------------------------------------------------------------------------------------
***Fig. 13.2e*** ***Fig. 13.2f***
------------------------------------------------------ ------------------------------------------------------
{width="3.2505271216097986in" {width="2.7720789588801398in"
height="3.3606167979002626in"} height="3.350340113735783in"}
-------------------------------------------------------------------------------------------------------------
The rainfall data are first examined briefly (as usual) with ***Climatic
\> Tidy and Examine \> One Variable Summaries.*** Use all the columns.
The results are shown in Fig. 13.2g. There is a problem with the station
WEN, where the minimum is -999.
-------------------------------------------------------------------------------------------------------------
***Fig. 13.2g*** ***Fig. 13.2h***
------------------------------------------------------ ------------------------------------------------------
{width="3.1101279527559056in" {width="2.8708475503062116in"
height="2.217218941382327in"} height="2.8815398075240597in"}
-------------------------------------------------------------------------------------------------------------
This could have been changed to a missing value when the data were
imported. Now the change is made with the dialogue ***Climatic \> Tidy
and Examine \> Replace Values***. Fig 13.2h.
Now stack the rainfall data using ***Climatic \> Tidy and Examine \>
Stack***, as shown in Fig. 13.2i.
Now use ***Describe \> Specific \> Line Plot***, as shown in Fig. 13.2j.
Include the ***Station*** as a ***facet***.
-------------------------------------------------------------------------------------------------------------
***Fig. 13.2i Climatic \> Tidy and Examine \>Stack*** ***Fig. 13.2j***
------------------------------------------------------ ------------------------------------------------------
{width="3.15838801399825in" {width="2.8473687664041996in"
height="2.91377624671916in"} height="2.88209208223972in"}
-------------------------------------------------------------------------------------------------------------
The results are roughly as shown in Fig. 13.2k. (If you would like to
get the results exactly as Fig. 13.2k, then either follow the note
below[^56] or open the file that is better prepared -- called
ghana1981-2014.rds and use the Climatic \> PICSA \> Rainfall Graph
dialogue.)
-----------------------------------------------------------------------
***Fig. 13.2k***
-----------------------------------------------------------------------
{width="6.268055555555556in"
height="3.057638888888889in"}
-----------------------------------------------------------------------
The stations go from South to North in Fig. 13.2k. We see that the most
Southerly station, Axim, is different to the other stations. The
variability of the few stations in the North of Ghana is much less than
those in the South. This is going to make the forecasting task much
harder to expect much that is meaningful for the North.
Next examine the correlations. They use the original data, but
unstacking the data with the Stations from South to North will put the
resulting columns in the same order.
Hence (assuming you have the data in this order) use Climatic \> Tidy
and Examine \> Unstack, as shown in Fig. 13.2l
------------------------------------------------------------------------------------------------------------
***Fig. 13.2l*** ***Fig. 13.2m***
------------------------------------------------------ -----------------------------------------------------
{width="3.0245745844269467in" {width="2.868203193350831in"
height="2.9575273403324585in"} height="3.0626574803149604in"}
------------------------------------------------------------------------------------------------------------
Next use ***Climatic \> Seasonal Forecast Support \> Correlations***.
Fig. 13.2m. The results provide further "food-for-thought. The most
Southerly station (bottom row in Fig 13.2m) and the most Northerly
(column to the right in Fig. 13.2m) each have quite a lot of blue
values, i.e. negative correlations. There are just 5 stations in the
North of Ghana (latitudes between 9°N and 11°N and the correlations
there are low. If 2 stations have a low or zero correlation, then
logically they should have a separate seasonal forecast. However, Fig.
13.1a shows the whole of the North has a single forecast.
With this information we would be inclined to
a) Omit Axim as it seems so different
b) Consider only using the stations from the South.
c) Query including Akatsi, which is the furtherst to the Eaqst and has
very low correlation with the other stations
d) Look for more rainfall stations from the North.
If, instread, all the stations are used in CPT, then the finalo stage is
a multiple regression on each y-variable separately, as a function of
the set of x-variables, and they are usually the principal components.
Then the interest would be more in the individual results at a station
level -- and these are given by CPT.
-----------------------------------------------------------------------
***Fig. 13.2n***
-----------------------------------------------------------------------
{width="5.91378280839895in"
height="5.039098862642169in"}
-----------------------------------------------------------------------
Finally, in ***Climatic \> Seasonal Forecast Support \> Correlations***
(Fig. 13.2m) use just the 5 columns from the North, (from Bole to
Navrongo) and opt for a pairwise plot. This shows the size of the
correlations clearly and confirms that the whole of the North should not
have a single forecast.
-----------------------------------------------------------------------
***Fig. 13.2o***
-----------------------------------------------------------------------
{width="6.112517497812774in"
height="3.49576990376203in"}
-----------------------------------------------------------------------
## Rainfall data with many stations
The second example is from Rwanda. The rainfall data are considered in
this section. The data file is again in a form that reads directly into
CPT. The file, in Excel, is shown in Fig. 13.3a. These data are again
3-month rainfall totals and are from March to May. They are for 37
years, from 1981 to 2017.
These are estimated rainfall from ENACTS. This is a merged product,
combining station data with estimated rainfall from satellite
observations (Siebert, et al., 2019). In Fig. 13.3a the first column
gives the latitude and row 5 gives the longitude of each grid point. So,
the estimated rainfall total at 1.05°S and 28.54°E in 1981 was 550mm.
------------------------------------------------------------------------------------------------------------
***Fig. 13.3a*** ***Fig. 13.3b File \> Open***
------------------------------------------------------ -----------------------------------------------------
{width="3.004711286089239in" {width="2.9594510061242345in"
height="2.948018372703412in"} height="3.2666458880139984in"}
------------------------------------------------------------------------------------------------------------
In the data in Fig. 13.3a the rectangle of data for 1981 is followed by
an approximate repeat of lines 4 and 5, followed by the data for 1982.
And so on to 2017.
If the data, from Excel are saved, then the default (by Excel) is to add
the ***txt*** extension and this makes it easy to import into R-Instat.
In R-Instat use ***File \> Open***, Fig. 13.3b. Change the ***Lines to
Skip*** to 4, so the first line is the longitudes.
------------------------------------------------------------------------------------------------------------
***Fig. 13.3c*** ***Fig. 13.3d Setting the filter***
------------------------------------------------------ -----------------------------------------------------
{width="2.938659230096238in" {width="2.9718602362204725in"
height="3.8734087926509186in"} height="2.960559930008749in"}
------------------------------------------------------------------------------------------------------------
These data, in Fig. 13.3c, need tidying. The first step is to delete the
rows between each year. This uses a filter, so right click, choose
Filter and then define a new filter on the first column. Part of the
filter sub-dialogue is shown in Fig. 13.3d.
When you return to the main dialogue, Fig. 13.3e choose to make the
filtered data a subset. If you feel bold, then give the new name the
same as the old one, so the original file is overwritten.
There are now 1924 rows of data, i.e. 52 rows each year, for 37 years.
Now a year variable is added as shown in Fig. 13.3f. Check, Fig. 13.3f,
that it will be the same length as the other columns of data.
------------------------------------------------------------------------------------------------------------
***Fig. 13.3e Making a subset*** ***Fig. 13.3f Adding a year variable***
------------------------------------------------------ -----------------------------------------------------
{width="2.4592377515310586in" {width="3.5354002624671916in"
height="2.761431539807524in"} height="2.9525820209973754in"}
------------------------------------------------------------------------------------------------------------
Now all that remains is to stack the data, ***Climatic \> Tidy and
Examine \> Stack***, as shown in Fig. 13.3g. The re4sulting data are in
Fig.13.3h. There are now 126984 rows of data, i.e. 37 years from 52 \*
66 = 3432 equally spaced locations.
------------------------------------------------------------------------------------------------------------
***Fig. 13.3g*** ***Fig. 13.3h The Rwanda ENACTS data so far***
------------------------------------------------------ -----------------------------------------------------
{width="2.946774934383202in" {width="2.965952537182852in"
height="2.53537510936133in"} height="3.399851268591426in"}
------------------------------------------------------------------------------------------------------------
We outline further "housekeeping" steps on these data to make it simpler
to examine and to export back to CPT when needed:
a) Use ***Prepare \> Column: Text \> Transform \> Substring*** on the
variable ***Lat*** into ***LatS*** from Start Value 2 to End Value
5.
b) Recall the ***last dialogue*** and put ***Lon*** into ***LonE***
from 2 to 6.
c) ***Select*** both these columns, (LatS and LonE), then
***right-click*** and make them ***Factors***.
d) Use ***Prepare \> Column: Factor: Factor \> Combine Factors***.
Choose ***LatS and LonE***, make the separator an ***underscore***
and make the ***New Column Name:*** ***Location***.
e) Select LatS and LonE again. Right-click and ***Convert to Numeric***
columns.
f) Use ***Prepare \> Column: Factor \> Recode Numeric*** and make a new
column from ***Lats*** into ***Lat6S***, with 10 break points at
about (1.03, 1.25, 1.48, 1.7,1.93, 2.15, 2.38, 2.6, 2.83, 2.98).
g) Recall the last dialogue and make LonE into Lon6E using (28.5,
28.74, 28.97, 29.2, 29.42, 29.64, 29.87, 30.1, 30.32, 30.54, 30.77,
31).
h) Right click to delete the 2 columns Lat, Lon.
i) Reorder the columns possibly as shown in Fig. 13.3i
------------------------------------------------------------------------------------------------------------
***Fig. 13.3i ENACTS data for Rwanda*** ***Fig. 13.3j The locations***
----------------------------------------------------- ------------------------------------------------------
{width="3.459744094488189in" {width="2.6555074365704288in"
height="2.7487062554680666in"} height="2.722613735783027in"}
------------------------------------------------------------------------------------------------------------
A Station (i.e. Location data frame is also needed for exporting back to
CPT. From here:
a) ***Right-click*** and choose ***Filter*** on the year column and put
just the first year (1981) into a new data frame called
***Location***.
b) Delete the ***year and rain*** variables from the Location data
frame.
The resulting data frame is in Fig. 13.3j.
Now look at the at the data. Start with a given part of Rwanda.
Right-click and filter the data file to the ***last set of stations in
Lat6S*** and ***Lon6E***, i.e. the South-East corner. This is a 30km
square and there should be 880 rows of data, Fig. 13.3k.
-------------------------------------------------------------------------------------------------------------
***Fig. 13.3k SE corner (24 locations)*** ***Fig. 13.3l***
------------------------------------------------------ ------------------------------------------------------
{width="3.0264523184601924in" {width="2.8941546369203848in"
height="2.2105172790901135in"} height="2.9555139982502188in"}
-------------------------------------------------------------------------------------------------------------
These data can now be graphed. The results from a ***Describe \>
Specific \> Line Plot*** of ***rain*** against ***year*** by
***location*** is in Fig. 13.3l. (A facetted graph by LonE and LatS,
after making them factors, is an alternative).
Fig. 13.3l the coherence (high correlation) between the different
locations is clear. The last point (data from 2017) is a cause for
concern. This is also indicated for 4 of the locations in Fig. 13.3k.
This last year has less than half the rain of any of the other 36 years
at most locations. That can greatly affect a regression model. Perhaps
only fit using the data to 2016?
Next, use ***Climatic \> Tidy and Examine \> Unstack*** for the
***rain***, by the ***location*** and ***carry the year***. This gives
the 24 stations in separate columns and ***Climatic \> Seasonal Forecast
Support \> Correlations***, gives the results in Fig. 13.3m. They are
all coloured dark red (compare with Fig. 13.2n) as all correlations are
more than 0.8.
-----------------------------------------------------------------------
***Fig. 13.3m***
-----------------------------------------------------------------------
{width="5.9061286089238845in"
height="5.168680008748907in"}
-----------------------------------------------------------------------
This can be repeated for further parts of Rwanda. We suggest that
exporting the data from individual "blocks" of 24 or usually 36 stations
for CPT, may enable separate local forecasts to be given?
Change the filter to choose 12 blocks over the country, possibly Lat6S =
(1, 5, 9) and Lon6E = (1, 4, 7, 10).
-------------------------------------------------------------------------------------------------------------
***Fig. 13.3n Choosing 12 blocks as a filter*** ***Fig. 13.3o Facet with 2 variables***
------------------------------------------------------ ------------------------------------------------------
{width="3.6805905511811026in" {width="2.402188320209974in"
height="2.7163943569553806in"} height="2.6810597112860894in"}
-------------------------------------------------------------------------------------------------------------
-----------------------------------------------------------------------
***Fig. 13.3p***
-----------------------------------------------------------------------
{width="6.268055555555556in"
height="3.0805555555555557in"}
-----------------------------------------------------------------------
The results in Fig. 13.3p show some part of the country, e.g. North-West
-- (top-left) with very high correlations, but also relatively little
year-to-year variability to be explained, compared to other parts. (The
blue set of graphs in the middle of Fig. 13.3p should be examined in
more detail, as the large rainfall in about 1990 is just in a few
locations -- perhaps caused by data from a single station?). The low
rainfall totals in 2017, mentioned above, is apparent in some parts of
the country, but not all.
Plots of further combinations could be useful. Then 2 alternative
strategies for CPT (in addition to the default of using the 3432
stations individually) could be:
a) Use data from single blocks of interest, i.e. usually 36 locations
over a 30km by 30km grid, to examine the forecast for specific parts
of the country.
b) Take the means (or medians) each year, for each of the blocks, so
reducing the number of locations to 96 and use these data instead of
the data individually for the 3432 locations.
## The X variables -- Sea Surface Temperatures
Ghana data first.
Then Rwanda data!
For Rwanda data use
[[http://iridl.ldeo.columbia.edu/SOURCES/.IRI/.Analyses/.ICPAC/.Models/.GFDL/.GFDL-CM2p5-FLOR-A06/.MONTHLY/.sst/index.html]{.underline}](http://iridl.ldeo.columbia.edu/SOURCES/.IRI/.Analyses/.ICPAC/.Models/.GFDL/.GFDL-CM2p5-FLOR-A06/.MONTHLY/.sst/index.html)
The data were downloaded from this
link [[http://iridl.ldeo.columbia.edu/SOURCES/.Models/.NMME/.GFDL-CM2p5-FLOR-A06/.MONTHLY/.sst/]{.underline}](http://iridl.ldeo.columbia.edu/SOURCES/.Models/.NMME/.GFDL-CM2p5-FLOR-A06/.MONTHLY/.sst/)
However you may decide to choose any other model of your choice.
Those Sea Surface Temperature (SST) are GCM outputs from different
source (GFDL, CFS2, NASA etc). Initialization is the process of locating
and using the defined values for variable data that is used by a model
or system. For our model we choose February as the month forecasts (MAM)
were initialized.