I would probably do something like this to make an array of hashrefs.

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11160609
use warnings;
use List::AllUtils qw( pairwise bundle_by );

my @keys = split /, /, 'Pressure, Geop Height, Temperature, Dew Point,
+ Humidity, Wind Direction, Wind Speed MS, Wind UMS, Wind VMS, Precipi
+tation Amount, Total Cloud Cover, Low Cloud Cover, Medium Cloud Cover
+, High Cloud Cover, Radiation Global, Radiation Global Accumulation, 
+Radiation Net Surface LW Accumulation, Radiation Net Surface SW Accum
+ulation, Radiation SW Accumulation, Visibility, Wind Gusts';

my @datasets = bundle_by {
  +{ pairwise { $a, $b } @keys, @_ }
  } 21, split ' ', getdata();

use Data::Dump 'dd'; dd @datasets[0 .. 2];

sub getdata {
return '1016.1 7.7 20.6 13.8 72.9 215.0 6.64 3.94 5.33 0.0 31.3 31.3 0
+.0 0.0
...
10727690.0 38242.3 10.8';
}
[download]

And here's what the first 3 elements of the answer array are:

(
  {
    "Dew Point"                             => 13.8,
    "Geop Height"                           => 7.7,
    "High Cloud Cover"                      => "0.0",
    "Humidity"                              => 72.9,
    "Low Cloud Cover"                       => 31.3,
    "Medium Cloud Cover"                    => "0.0",
    "Precipitation Amount"                  => "0.0",
    "Pressure"                              => 1016.1,
    "Radiation Global"                      => 716.7,
    "Radiation Global Accumulation"         => "8461717.0",
    "Radiation Net Surface LW Accumulation" => "NaN",
    "Radiation Net Surface SW Accumulation" => "7750386.0",
    "Radiation SW Accumulation"             => "2224256.0",
    "Temperature"                           => 20.6,
    "Total Cloud Cover"                     => 31.3,
    "Visibility"                            => 38507.5,
    "Wind Direction"                        => "215.0",
    "Wind Gusts"                            => 10.9,
    "Wind Speed MS"                         => 6.64,
    "Wind UMS"                              => 3.94,
    "Wind VMS"                              => 5.33,
  },
  {
    "Dew Point"                             => 13.7,
    "Geop Height"                           => 7.7,
    "High Cloud Cover"                      => "0.0",
    "Humidity"                              => 71.1,
    "Low Cloud Cover"                       => 2.1,
    "Medium Cloud Cover"                    => "0.0",
    "Precipitation Amount"                  => "0.0",
    "Pressure"                              => 1016.4,
    "Radiation Global"                      => 727.6,
    "Radiation Global Accumulation"         => "11081057.0",
    "Radiation Net Surface LW Accumulation" => "NaN",
    "Radiation Net Surface SW Accumulation" => "10146792.0",
    "Radiation SW Accumulation"             => 2372829.8,
    "Temperature"                           => 21.1,
    "Total Cloud Cover"                     => 2.1,
    "Visibility"                            => 40682.2,
    "Wind Direction"                        => "222.0",
    "Wind Gusts"                            => 11.2,
    "Wind Speed MS"                         => 6.82,
    "Wind UMS"                              => 4.67,
    "Wind VMS"                              => 4.95,
  },
  {
    "Dew Point"                             => 13.2,
    "Geop Height"                           => 7.7,
    "High Cloud Cover"                      => "0.0",
    "Humidity"                              => 67.7,
    "Low Cloud Cover"                       => 0.8,
    "Medium Cloud Cover"                    => "0.0",
    "Precipitation Amount"                  => "0.0",
    "Pressure"                              => 1016.4,
    "Radiation Global"                      => 749.9,
    "Radiation Global Accumulation"         => "13780637.0",
    "Radiation Net Surface LW Accumulation" => "NaN",
    "Radiation Net Surface SW Accumulation" => "12614863.0",
    "Radiation SW Accumulation"             => 4011495.3,
    "Temperature"                           => 21.6,
    "Total Cloud Cover"                     => 0.8,
    "Visibility"                            => 44407.4,
    "Wind Direction"                        => "220.0",
    "Wind Gusts"                            => 11.3,
    "Wind Speed MS"                         => 6.71,
    "Wind UMS"                              => 4.37,
    "Wind VMS"                              => 5.1,
  },
)
[download]

I would first split and then process in chunks of 21 items:

my @values = split /\s+/, $weatherdata;
croak "Invalid item count in weather data"
    unless @values % 21 == 0;
while(my @row = splice @values, 0, 21 ) {
....
}
[download]

Is there a way to use split on blocks of 21 items at a time?

Sure -- ask for the first 22 blocks (n+1) using split, then re-do the process with the last block (which will will contain the remaining bits). Repeat until you're out of blocks.