So, you have K m is nothing but wave number for that frequency component you have to K is nothing but you already know K is 2 pi by L and L is going to be a function of frequency. So, naturally you will have to calculate your k and t is the time and then
epsilon m is the random phase angle distributed uniformly between 0 to 2 pi which I have already explained under random waves. So, this K m is related to the dispersion relationship as indicated here x and y are coordinates horizontal coordinates at which the surface elevation is being considered at any location x or y, so this general expression rho x u the description of wave elevation very clearly, it has considered the frequency components, it has considered the direction of components and it has also accommodated a particular location in as a function location. So, this is in its generalized form the representation of wave profile.