## 1. Introduction

[2] Tidal dynamics in coastal aquifers plays a role in numerous environmental issues in coastal and estuarine areas, such as saltwater intrusion, contaminant transformation and migration, control of erosion and biological activities [*Cheng and Ouazar*, 2004]. Numerous analytical solutions for modeling of tide-induced groundwater fluctuations are available, which take into account the effect of the vertical beach, sloping beach, aquifer leakage, density differences and varying tidal signal along the estuary [e.g., *Nielsen*, 1990; *Li et al.*, 2000a; *Teo et al.*, 2003]. Most analytical solutions are based on the assumption of monochromatic tides, which may over simplify the tidal wave conditions. In reality, tides are more complicated and often bichromatic, containing oscillations of at least two different frequencies. For example, in Ardeer, Scotland, a semidiurnal solar tide has period *T*_{1} = 12 hours and frequency ?_{1} = 0.5236 rad/h, while *T*_{2} = 12.42 hours and ?_{2} = 0.5059 rad/h for a semidiurnal lunar tide (X. Mao et al., Tidal influence on behaviour of a coastal aquifer adjacent to a low-relief estuary, submitted to *Journal of Hydrology*, 2005, hereinafter referred to as Mao et al., submitted manuscript, 2005). As a result, the spring-neap cycle (i.e., the tidal envelope) is formed with a longer period, *T*_{sn} = 2p/(?_{1} − ?_{2}) = 14.78 days. The nonlinear propagation of the bichromatic tides in the aquifer results in low-frequency water table fluctuations over the spring-neap period, as has been measured in the field by *Raubenheimer et al.* [1999] and demonstrated mathematically by *Li et al.* [2000b]. These low-frequency water table fluctuations, called spring-neap tidal water table fluctuations hereafter, propagated much further inland than the primary tidal signals (i.e., diurnal and semidiurnal tides). Such fluctuations have been analyzed recently [*Li et al.*, 2000b; *Su et al.*, 2003], with results demonstrating the effects of interacting tidal components. However, these results were based on only the zeroth-order shallow water expansion, i.e., the Bouniessq equation, which may be insufficient for some tidal conditions [*Teo et al.*, 2003].

[3] The objective of this note is to extend these results by deriving an analytical solution for spring-neap tide-induced water table fluctuations in a sloping sandy beach, based on a higher-order shallow water expansion. The proposed analytical solution will be compared briefly with field observations from Adreer, Scotland (Mao et al., submitted manuscript, 2005), and previous analytical solution based on Boussinesq equation [*Li et al.*, 2000b]. Then a parametric study to investigate the influence of amplitude ratio, frequency ratio and phases is conducted.