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Zhiling Liao
,
Shaowu Li
,
Ye Liu
, and
Qingping Zou
Free access
Zhiling Liao
,
Shaowu Li
,
Ye Liu
, and
Qingping Zou

Abstract

The theoretical model for group-forced infragravity (IG) waves in shallow water is not well established for nonbreaking conditions. In the present study, analytical solutions of the group-forced IG waves at O(β 1) (β 1 = h x /(Δkh), h x = bottom slope, Δk = group wavenumber, h = depth) in intermediate water and at O ( β 1 1 ) in shallow water are derived separately. In case of off-resonance [β 1 μ −1 = O(β 1), where μ = 1 c g 2 / ( g h ) is the resonant departure parameter, c g = group speed] in intermediate water, additional IG waves in quadrature with the wave group forcing (hereinafter, the nonequilibrium response or component) are induced at O(β 1) relative to the equilibrium bound IG wave solution of Longuet–Higgins and Stewart (1962) in phase with the wave group. The present theory indicates that the nonequilibrium response is mainly attributed to the spatial variation of the equilibrium bound IG wave amplitude instead of group-forcing. In case of near-resonance [β 1 μ −1 = O(1)] in shallow water; however, both the equilibrium and nonequilibrium components are ~ O ( β 1 1 ) at the leading order. Based on the nearly-resonant solution, the shallow water limit of the local shoaling rate of bound IG waves over a plane sloping beach is derived to be ~h −1 for the first time. The theoretical predictions compare favorably with the laboratory experiment by Van Noorloos (2003) and the present numerical model results generated using SWASH. Based on the proposed solution, the group-forced IG waves over a symmetric shoal are investigated. In case of off-resonance, the solution predicts a roughly symmetric reversible spatial evolution of the IG wave amplitude, while in cases of near to full resonance the IG wave is significantly amplified over the shoal with asymmetric irreversible spatial evolution.

Open access
Fang Wang
,
Quansheng Ge
,
Shaowu Wang
,
Qingxiang Li
, and
Philip D. Jones

Abstract

The extent to which an urbanization effect has contributed to climate warming is under debate in China. Some previous studies have shown that the urban heat island (UHI) contribution to national warming was substantial (10%–40%). However, by considering the spatial scale of urbanization effects, this study indicates that the UHI contribution is negligible (less than 1%). Urban areas constitute only 0.7% of the whole of China. According to the proportions of urban and rural areas used in this study, the weighted urban and rural temperature averages reduced the estimated total warming trend and also reduced the estimated urban effects. Conversely, if all stations were arithmetically averaged, that is, without weighting, the total warming trend and urban effects will be overestimated as in previous studies because there are more urban stations than rural stations in China. Moreover, the urban station proportion (68%) is much higher than the urban area proportion (0.7%).

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