Tiny pressure gradient forces caused by hydrostatic truncation error can overwhelm minuscule pressure gradients that drive shallow nocturnal drainage winds in a mesobeta numerical model. In seeking a method to reduce these errors, a mathematical formulation for pressure gradient force errors was derived for a single coordinate surface bounded by two pressure surfaces. A nonlinear relationship was found between the lapse rate of temperature, the thickness of the bounding pressure layer, the slope of the coordinate surface and the location of the coordinate surface within the pressure layer. The theory shows that pressure gradient force error can be reduced in the numerical model if column pressures are sums of incremental pressures over shallow layers. A series of model simulations verify the theory and show that the theory explains the only source of pressure gradient force error in the model. Abstract Tiny pressure gradient forces caused by hydrostatic truncation error can overwhelm minuscule pressure gradients that drive shallow nocturnal drainage winds in a mesobeta numerical model. In seeking a method to reduce these errors, a mathematical formulation for pressure gradient force errors was derived for a single coordinate surface bounded by two pressure surfaces. A nonlinear relationship was found between the lapse rate of temperature, the thickness of the bounding pressure layer, the slope of the coordinate surface and the location of the coordinate surface within the pressure layer. The theory shows that pressure gradient force error can be reduced in the numerical model if column pressures are sums of incremental pressures over shallow layers. A series of model simulations verify the theory and show that the theory explains the only source of pressure gradient force error in the model.