Precipitation Isosceles Triangle (PITRI): A Simple Approach for Approximating the Diurnal Cycle of Precipitation for Use in Hydrological Simulations

Accurate characterization of precipitation (P) at hourly temporal resolution is important for a wide range of hydrological applications, ranging from flood risk assessment and engineering design at small scales to investigation of water and energy cycles at large scales. Unfortunately, gridded observational datasets of sufficient length and spatial coverage for these studies are only available for daily total P. While stochastic and dynamical downscaling methods have been employed to disaggregate P from daily totals, these methods involve large numbers of uncertain parameters and computational costs. On the other hand, a common deterministic disaggregation approach, in which the daily total P is distributed uniformly across all hours, is grossly inaccurate in representing the diurnal cycle. Accordingly, a deterministic approach that represents the diurnal cycle of P more accurately is needed.

Here we present the Precipitation Isosceles Triangle (PITRI) method, a two-parameter deterministic approach in which the hourly hyetograph is modeled with an isosceles triangle with prescribed duration and time of peak intensity. Duration and peak time are each assigned 12 monthly values obtained from climatological mean monthly observations at United States Climate Reference Network (USCRN) stations, and extended to all points in space via linear regression against historical climate statistics.

We evaluated the performance of the PITRI approach by running three sets of simulations using the Variable Infiltration Capacity (VIC) model at 128 USCRN stations, driven by the same observed meteorology, but with hourly P (a) derived from observations (Pobs), (b) disaggregated uniformly across all hours (Puni), and (c) disaggregated from daily total via PITRI. Relative to simulations driven by Pobs, the Puni approach substantially underestimated daily peak P intensities (Pmax), peak runoff (Qmax) and daily total runoff (Qday), leading to underestimates of annual total runoff (Qann) of 11% on average. In contrast, PITRI reproduced Pmax, Qmax, and Qday with relatively little bias for all but the largest values, leading to biases in Qann of less than 1% on average. Comparing gridded simulations using Puni and PITRI at 1/16 degree (6 km) resolution over the continental US, southern Canada, and Mexico, for the period 1981-2013, we found that absolute differences in Qann were strongly correlated with annual precipitation, being largest in the US and Canada east of 100 W longitude and in southern and eastern Mexico. One exception to this pattern was in the Pacific Northwest, where long event durations led to similar results between the two methods. The PITRI approach therefore should provide substantial improvements in accuracy over the commonly used uniform approach in most climates.