Fade an element out when scrolling down and fade in it back when scrolling up. Source: StudioPress Agency Pro child theme.

fade-out-fade-in.php

<?php

add_action('wp_enqueue_scripts', 'agency_enqueue_scripts');
/**
 * Enqueue Scripts
 */
function agency_enqueue_scripts() {
    
    if (is_active_sidebar('home-top') || is_active_sidebar('home-middle') || is_active_sidebar('home-bottom')) {
        
        wp_enqueue_script('scrollTo', get_stylesheet_directory_uri() . '/js/jquery.scrollTo.min.js', array('jquery'), '1.4.5-beta', true);
        wp_enqueue_script('home', get_stylesheet_directory_uri() . '/js/home.js', array('localScroll'), '', true);
    }
}

home.js

jQuery(function($) {
    function fade_home_top() {
        if ($(window).width() > 800) {
            window_scroll = $(this).scrollTop();
            $(".home-top").css({
                'opacity': 1 - (window_scroll / 300)
            });
        }
    }
    $(window).scroll(function() {
        fade_home_top();
    });
});

jquery.scrollTo.min.js

/**
 * Copyright (c) 2007-2012 Ariel Flesler - aflesler(at)gmail(dot)com | http://flesler.blogspot.com
 * Dual licensed under MIT and GPL.
 * @author Ariel Flesler
 * @version 1.4.5 BETA
 */
;(function($){var h=$.scrollTo=function(a,b,c){$(window).scrollTo(a,b,c)};h.defaults={axis:'xy',duration:parseFloat($.fn.jquery)>=1.3?0:1,limit:true};h.window=function(a){return $(window)._scrollable()};$.fn._scrollable=function(){return this.map(function(){var a=this,isWin=!a.nodeName||$.inArray(a.nodeName.toLowerCase(),['iframe','#document','html','body'])!=-1;if(!isWin)return a;var b=(a.contentWindow||a).document||a.ownerDocument||a;return/webkit/i.test(navigator.userAgent)||b.compatMode=='BackCompat'?b.body:b.documentElement})};$.fn.scrollTo=function(e,f,g){if(typeof f=='object'){g=f;f=0}if(typeof g=='function')g={onAfter:g};if(e=='max')e=9e9;g=$.extend({},h.defaults,g);f=f||g.duration;g.queue=g.queue&&g.axis.length>1;if(g.queue)f/=2;g.offset=both(g.offset);g.over=both(g.over);return this._scrollable().each(function(){if(e==null)return;var d=this,$elem=$(d),targ=e,toff,attr={},win=$elem.is('html,body');switch(typeof targ){case'number':case'string':if(/^([+-]=?)?\d+(\.\d+)?(px|%)?$/.test(targ)){targ=both(targ);break}targ=$(targ,this);if(!targ.length)return;case'object':if(targ.is||targ.style)toff=(targ=$(targ)).offset()}$.each(g.axis.split(''),function(i,a){var b=a=='x'?'Left':'Top',pos=b.toLowerCase(),key='scroll'+b,old=d[key],max=h.max(d,a);if(toff){attr[key]=toff[pos]+(win?0:old-$elem.offset()[pos]);if(g.margin){attr[key]-=parseInt(targ.css('margin'+b))||0;attr[key]-=parseInt(targ.css('border'+b+'Width'))||0}attr[key]+=g.offset[pos]||0;if(g.over[pos])attr[key]+=targ[a=='x'?'width':'height']()*g.over[pos]}else{var c=targ[pos];attr[key]=c.slice&&c.slice(-1)=='%'?parseFloat(c)/100*max:c}if(g.limit&&/^\d+$/.test(attr[key]))attr[key]=attr[key]<=0?0:Math.min(attr[key],max);if(!i&&g.queue){if(old!=attr[key])animate(g.onAfterFirst);delete attr[key]}});animate(g.onAfter);function animate(a){$elem.animate(attr,f,g.easing,a&&function(){a.call(this,e,g)})}}).end()};h.max=function(a,b){var c=b=='x'?'Width':'Height',scroll='scroll'+c;if(!$(a).is('html,body'))return a[scroll]-$(a)[c.toLowerCase()]();var d='client'+c,html=a.ownerDocument.documentElement,body=a.ownerDocument.body;return Math.max(html[scroll],body[scroll])-Math.min(html[d],body[d])};function both(a){return typeof a=='object'?a:{top:a,left:a}}})(jQuery);