Background Peak flow rate in watersheds is a critical parameter for soil erosion modeling and the design of soil and water conservation projects. In China, research on the formula to predict peak flow rate has primarily focused on the Loess Plateau. However, in the Black Soil Region of Northeast China, where soil erosion is severe, there is a lack of empirical formulas to predicting peak flow rate. The purpose of this study are to develop a formula to predict the peak flow rate in the Black Soil Region of Northeast China.

Methods A total of 120 rainfall events were collected across nine watersheds of the Black Soil Region of Northeast China from 2011-2012 and 2017-2019. The data was divided into two sets. The first set, comprising 95 events, were used to develop a new formula, while the second set, consisting of 25 events, was used to validate the equations. Pearson correlation analysis were conducted between peak flow rate and various effect factors, including rainfall, maximum 60-minute rainfall intensity (I₆₀), average rainfall intensity, watershed area, watershed length, channel slope, runoff depth, and runoff coefficient. Existing formulas for predicting peak flow rates were tested in the region, and the new equations were developed using the dimensionless analyses and nonlinear regression methods.

Results Existing formulas for predicting peak flow rates, such as that used in Chemical, Runoff, and Erosion Modeling in Agricultural Management Systems (CREAMS) and on the Loess Plateau, significantly overestimated the peak flow rates in the Black Soil Region of Northeast China. The peak flow rate was found to be significantly correlated with rainfall depth, maximum 60-minute rainfall intensity (I₆₀), average rainfall intensity, runoff depth and channel slope at the 0.01 confidence level. A new formula for predicting peak flow rates was developed, with independent variables including rainfall depth, I₆₀, runoff depth, channel slope and drainage area. The model efficiency was 0.68 when calibrated using the first data set and 0.78 when validated with the second dataset. Considering that obtaining I₆₀ data can sometimes be challenging, an alternative equation excluding I₆₀ as an independent variable was developed. The model efficiency for this alternative formula was 0.67 when calibrated with the first dataset and 0.78 when validated with the second dataset.

Conclusions The results indicate that the both formulas effectively predict the peak flow rates in the study watersheds. However, their applicability is limited when the effective precipitation or the maximum 60-min rainfall intensity reaches extremely high or low. This study provides important contributions to the hydrological analysis in the Black Soil Region of Northeast China, and offers methodological support for regional soil erosion simulations and the design of soil and water conservation engineering projects.