Wastewater-based surveillance is an important tool for monitoring the COVID-19 pandemic. However, it remains challenging to translate wastewater SARS-CoV-2 viral load to infection number, due to unclear shedding patterns in wastewater and potential differences between variants. We utilized comprehensive wastewater surveillance data and estimates of infection prevalence (i.e., the source of the viral shedding) available for New York City (NYC) to characterize SARS-CoV-2 fecal shedding pattern over multiple COVID-19 waves. We collected SARS-CoV-2 viral wastewater measurements in NYC during August 31, 2020 - August 29, 2023 ( N = 3794 samples). Combining with estimates of infection prevalence (number of infectious individuals including those not detected as cases), we estimated the time-lag, duration, and per-infection fecal shedding rate for the ancestral/Iota, Delta, and Omicron variants, separately. We also developed a procedure to identify occasions with intensified transmission. Models suggested fecal viral shedding likely starts around the same time as and lasts slightly longer than respiratory tract shedding. Estimated fecal viral shedding rate was highest during the ancestral/Iota variant wave, at 1.44 (95% CI: 1.35 - 1.53) billion RNA copies in wastewater per day per infection (measured by RT-qPCR), and decreased by ∼20% and 50-60% during the Delta wave and Omicron period, respectively. We identified around 200 occasions during which the wastewater SARS-CoV-2 viral load exceeded the expected level in any of 14 sewersheds. These anomalies disproportionally occurred during late January, late April - early May, early August, and from late-November to late-December, with frequencies exceeding the expectation assuming random occurrence ( P < 0.05; bootstrapping test). These estimates may be useful in understanding changes in underlying infection rate and help quantify changes in COVID-19 transmission and severity over time. We have also demonstrated that wastewater surveillance data can support the identification of time periods with potentially intensified transmission.