JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<h1>Choose Model and Timeframe</h1>
<h2> <select name="category" id='dropdown1'>
    <option value="0" rel='start'>Select Model</option>
    <option value="1" rel="GFS">GFS</option>
    <option value="2" rel="NAM">NAM</option>
</select>

<select name="items" class="cascade", id="imgList" style='display:none'>
    <option value="" class='NAM'>Please select a timeframe</option>
    <option value="" class='GFS'>Please select a timeframe</option>
    <option value='Model_Data/GFS/meteogram/trends/images/NYC/gfs_1day_temp.png' class="GFS">1-Day</option>
    <option value='Model_Data/GFS/meteogram/trends/images/NYC/gfs_5day_temp.png' class="GFS">5-Days</option>
    <option value='Model_Data/NAM/meteogram/images/1_day/NYC/nam_1day_temp.png' class="NAM">1-Day</option>

JavaScript

$('#dropdown1').change(function() {

$('#imgList').css('display','block');

});

    $(document).ready(function(){
    var $cat = $('select[name=category]'),
    $category = $('select[name=items]');

    $cat.change(function(){
        
        var $this = $(this).find(':selected'),
        rel = $this.attr('rel');
                
        // Hide all
        $category.find("option").hide();
          
        // Find all matching accessories
        // Show all the correct accesories
        // Select the first accesory
        $set = $category.find('option.' + rel);
        $set.show().first().prop('selected', true);
        
    });
});

            function setClass() {
                var img = document.getElementById("image");
                img.src = this.value;
                return false;
            }
            document.getElementById("imgList").onchange = setClass;