A low order dynamical model for runoff predictability
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A low order dynamical model for runoff predictability Roman Olson1,2,3 · Axel Timmermann2,3 · June‑Yi Lee2,4 · Soon‑Il An1,5 Received: 11 December 2019 / Accepted: 2 October 2020 © The Author(s) 2020
Abstract Recent work has identified potential multi-year predictability in soil moisture (Chikamoto et al. in Clim Dyn 45(7–8):2213– 2235, 2015). Whether this long-term predictability translates into an extended predictability of runoff still remains an open question. To address this question we develop a physically-based zero-dimensional stochastical dynamical model. The model extends previous work of Dolgonosov and Korchagin (Water Resour 34(6):624–634, 2007) by including a runoff-generating soil moisture threshold. We consider several assumptions on the input rainfall noise. We analyze the applicability of analytical solutions for the stationary probability density functions (pdfs) and for waiting times for runoff under different assumptions. Our results suggest that knowing soil moisture provides important information on the waiting time for runoff. In addition, we fit the simple model to daily NCEP1 reanalysis output on a near-global scale, and analyze fitted model performance. Over many tropical regions, the model reproduces the simulated runoff in NCEP1 reasonably well. More detailed analysis over a single gridpoint illustrates that the model, despite its simplicity, is able to capture some key features of the runoff time series and pdfs of a more complex model. Our model exhibits runoff predictability of up to two months in advance. Our results suggest that there is an optimal predictability “window” in the transition zone between runoff-generating and dry conditions. Our model can serve as a “null hypothesis” model reference against more complex models for runoff predictability. Keywords Runoff · Threshold · Stochastical–dynamical model
1 Introduction There are several approaches to modelling and predicting water runoff (Nash and Sutcliffe 1970). The first approach is numerically simulating it using physical models (Chikamoto et al. 2015; Ajami et al. 2016; Kanamitsu et al. 2002; Nakaegwa 2008; Manabe 1969; Dai 2016; Beck et al. 2017, and others). The advantages of this approach is that these models are physically-based, and that they allow the runoff to be efficiently incorporated as a component of a complex climate * Roman Olson [email protected] 1
Irreversible Climate Change Research Center, Yonsei University, Seoul, South Korea
2
Center for Climate Physics, Institute for Basic Research, Busan, South Korea
3
Pusan National University, Busan, South Korea
4
Research Center for Climate Sciences, Pusan National University, Busan, South Korea
5
Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea
model, or reanalysis. The disadvantage is that numerical models are too complex to provide theoretical probability distributions for the runoff, or analytic expressions relevant for its predictability. The second approach is using statistical models (Mandelbrot and Wall
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