Figure 3. Co-occurrence probability between AMAX streamflow and (a) AMAX precipitation, (b) AMAX wet-month precipitation, (c) AMAX effective precipitation across all CAMELS catchments; and (d) when grouped into six categories using the fraction of precipitation falling as snow (fsnow ). Note that Peffwere available for only 638 catchments.
The vast majority of catchments (more than 95%) have a co-occurrence probability that is much higher than random chance (i.e., 2%), which is generally expected. Catchments with a relatively high co-occurrence probability are mostly located in coastal regions (e.g., South Atlantic-Gulf Region, Texas Gulf Region, California Region, and Pacific Northwest Region) while co-occurrence probability tends to be low whenever the fraction of precipitation falling as snow (fsnow ) is high (e.g., Upper Colorado Region and Great Basin Region). More importantly, only a small fraction (14%) of all catchments having a co-occurrence probability between QDOYMAX and PDOYMAX (Figure 3a; see Figure S6 for regional results) of at least 0.5, indicating a weak causal linkage.
The co-occurrence probability between QDOYMAX and Psm.DOYMAX (Figure 3b; see Figure S7 for regional results) is higher than or equal to 0.5 over 7% of all catchments, indicating a weaker causal linkage relative to that between QDOYMAX and PDOYMAX. A possible reason is that soil moisture has a relatively strong seasonal cycle [Eltahir , 1998; Findell and Eltahir , 1997], contrasting to a weak seasonality of short-duration precipitation extremes [Do et al. , 2020a]. Using Psm has potentially masked out many short-duration flood-induced rainfall events that spread throughout the years, leading to a lower co-occurrence probability. This finding suggests that precipitation extremes constrained over wet months has a potentially lower predictability for changes in annual floods.
Among the three precipitation extreme metrics, effective precipitation (Figure 3c; see Figure S8 for regional results) is the variable with the strongest causal relationship to floods. Specifically, 26% of all catchments have a co-occurrence probability between Peff.DOYMAX and QDOYMAX of at least 0.5. A simple approach to take into account snow-soil interaction has led to a substantial increase in co-occurrence probability, suggesting that catchment processes potentially play a more important role in modulating floods relative to precipitation intensity.
When catchments are divided into different categories usingfsnow (Figure 3d), there is a notable decrease of co-occurrence probability when fsnow increases. We note that the co-occurrence probability between precipitation extremes and floods is not consistently low across all catchments with a high fsnow . For instance, of all 73 catchments with an fsnow of higher than or equal to 0.5, six catchments (located in the Pacific Northwest Region) have a co-occurrence probability between PDOYMAX and QMAX of at least 0.5. As a result, catchments with a high snow-to-rain ratio are likely to have floods not driven by precipitation extremes, but there are exceptions such as catchments strongly influenced by atmospheric rivers which are responsible for flood-induced rainfall events.
3.3 To what extent are changes in precipitation extremes useful to explain changes in floods?
The co-variation between precipitation extremes and QMAXis relatively low, with 81%, 85%, and 66% of all catchments having an R2 of less than 0.5 for PMAX, Psm.MAX, and Peff.MAX respectively. When catchments are grouped into different categories according to co-occurrence probability, a strong positive correlation between co-variation and co-occurrence probability is observed (Figure 4). Of all catchments with co-occurrence probability of less than 0.5, the averaged R2 is 0.28 (for PMAX), 0.24 (for Psm.MAX) and 0.33 (for Peff.MAX) respectively, indicating that only about 30% of the temporal variability of floods can be explained by precipitation extremes.
Focusing on the catchments with the strongest causal relationship (i.e., a co-occurrence probability of at least 0.6), a low-to-moderate correlation is observed, with the median of R2 between QMAX and precipitation extremes is 0.41, 0.43 and 0.52 for PMAX, Psm.MAX and Peff.MAX respectively. The causal relationship between Peff.MAX and QMAX is the strongest, with 34 out of 63 catchments (54%) have an R2 of above 0.5. The relationship between PMAX and QMAX is the lowest, with 10 out of 28 catchments (36%) have an R2 value of above 0.5, further confirming the need for considering catchment processes (e.g., snow-soil interaction) to explain changes in annual floods.