The reason that happened is because the header image has a default height of 164px. This can be changed and adjusted on line 1710 in your CSS. I would start with around 84px like this –
.header-image .site-title a {
float: left;
min-height: 84px;
width: 100%;
}
Next, the other space is coming from the Search Widget in the Widget Area. You can either remove or adjust the padding on line 1725. I would start by adjusting the Top padding, and remove the bottom padding like this –
.header-image .site-header .widget-area {
padding: 20px 0 0;
}
Let me know if that helps