Analytical solutions are obtained for advection-dispersion equation in two-dimensional horizontal semi-infinite porous domains. The solute dispersion parameter is considered temporally dependent along uniform flow. The two main characteristic of the porous medium: desorption and reaction, both always some attenuation in solute concentration in liquid phase, are considered by retardation factor and first order decay term, respectively. The solutions are obtained for uniform and increasing input sources. New space and time variables are introduced to reduce the variable coefficients of the advection-dispersion equation into constant coefficients and Laplace transform technique is used to obtain the analytical solutions. The solution of the present problem is also derived in one and three-dimension. Physical significance of the problems is illustrated by different graphs.