# Establishing a Geological Knowledge Base for Braided River Deltas Using Google Earth
## 3 Results and Discussion
### Sedimentary Parameter Distribution Characteristics
#### 3.1.3 Nonlinear Wavelength-Amplitude Coupling  
Through fixed-point measurements and the fitting analysis of the channel width and amplitude in modern braided river deltas, functional relationships under different depositional backgrounds have been established, revealing distinct characteristics of the sediment supply, hydrodynamic conditions, and channel evolution:  
* 0.0027x + 321.49 (R\({}^{2}\) = 0.7446)
* Yukon-Kuskokwim Delta: y = 5 \(\times\) 10\({}^{-6}\)x\({}^{2}\) + 0.1558x + 635.12 (R\({}^{2}\) = 0.8706)
* Lena River: y = \(-\)5 \(\times\) 10\({}^{-6}\)x\({}^{2}\) + 0.3414x + 391.15 (R\({}^{2}\) = 0.5712)
* Po River: y = \(-\)3 \(\times\) 10\({}^{-6}\)x\({}^{2}\) + 0.3776x = 88.08 (R\({}^{2}\) = 0.9127)
* Poyang Lake: y = \(-\)2 \(\times\) 10\({}^{-5}\)x\({}^{2}\) + 0.4272x \(-\) 36.058 (R\({}^{2}\) = 0.6666)
* Orinoco: y = 7 \(\times\) 10\({}^{-6}\)x\({}^{2}\) + 0.2382x + 468.16 (R\({}^{2}\) = 0.8852)
* Rufiji River: y = \(-\)5 \(\times\) 10\({}^{-5}\)x\({}^{2}\) + 0.5874x \(-\) 115.71 (R\({}^{2}\) = 0.537)
* Saloum Delta: y = \(-\)9 \(\times\) 10\({}^{-6}\)x\({}^{2}\) + 0.4485x + 114.59 (R\({}^{2}\) = 0.7459)  
The Po River delta (R\({}^{2}\) = 0.9127) and Yukon-Kuskokwim delta (R\({}^{2}\) = 0.8706) show strong model fits, characterized by negative and positive quadratic coefficients, respectively. The Po River's negative quadratic term (\(-\)3 \(\times\) 10\({}^{-6}\)) suggests a decelerating growth of wavelength with increasing amplitude, likely influenced by wave-dominated delta destruction, where higher amplitudes (e.g., wave energy) constrain channel wavelength expansion. In contrast, the Yukon-Kuskokwim delta's positive quadratic term (5 \(\times\) 10\({}^{-6}\)) reflects an accelerating relationship, consistent with its river-dominated constructive setting, where the stable fluvial input promotes proportional increases in both wavelength and amplitude.  
Systems like the Rufiji River delta (R\({}^{2}\) = 0.537) and Lena River delta (R\({}^{2}\) = 0.5712) exhibit weak model performance, attributed to complex depositional dynamics. The Rufiji River's steep positive linear term (0.5874) and highly negative quadratic term (\(-\)5 \(\times\) 10\({}^{-5}\))  
Figure 5: Amplitude distribution and comprehensive data of eight groups of braided river deltas.  
indicate a concave-down relationship, possibly driven by intense tidal reworking that limits wavelength growth at large amplitudes. The Lena River's low R\({}^{2}\) may reflect ice-rich sediment characteristics and seasonal discharge fluctuations, introducing noise into morphometric measurements.  
Equations with positive quadratic terms (e.g., Wax Lake: 4 \(\times\) 10\({}^{-5}\); Orinoco: 7 \(\times\) 10\({}^{-6}\)) suggest wavelength increases superlinearly with amplitude, typical of constructive deltas where fluvial processes dominate and the sediment supply outpaces reworking. This supports the hypothesis that unidirectional fluvial energy promotes scalable channel patterns.  
Negative quadratic terms (e.g., Saloum delta: \(-9\times 10^{-6}\); Po River: \(-3\times 10^{-6}\)) indicate sublinear wavelength-amplitude scaling, characteristic of destructive deltas influenced by tidal or wave energy. Here, the increased amplitude (e.g., tidal range) introduces lateral channel migration or bifurcation, decoupling wavelength from simple quadratic scaling.  
While quadratic regression effectively captures first-order relationships in stable depositional environments, its applicability diminishes in systems with complex hydrodynamics or measurement uncertainties (e.g., Rufiji River delta, R\({}^{2}\) = 0.537). The quadratic framework provides a useful first approximation but must be contextualized within delta-specific depositional mechanisms. Regional variability in model performance highlights the need for process-based mechanistic models rather than universal empirical fits.