I don’t see any white space. Are you referring to the border under the header? If so, you can remove it from around line 1115 in your CSS –
.site-header {
background-color: #222222;
border-bottom: 1px solid #ddd;
left: 0;
position: fixed;
top: 0;
width: 100%;
z-index: 999;
}
Let me know if you’re referring to something else.