# Stochastic Analysis of the Marginal and Dependence Structure of Streamflows: From Fine-Scale Records to Multi-Centennial Paleoclimatic Reconstructions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Second-Order Dependence Structure Metrics

#### 2.2. Marginal Structure Metrics

#### 2.3. Global-Scale Data Extraction and Processing

^{2}.

## 3. Results

^{0.9}(R

^{2}= 0.28 when including all values; and R

^{2}= 0.87 when the reconstructed time series with the largest standard deviation value is omitted, which was causing a large residual value compared to the total sum of residuals between the model and data-values; see circled value in Figure 2), and k = 3.4 s

^{1.7}(R

^{2}= 0.97) when all values are included and k = 2.9 s

^{1.8}(R

^{2}= 0.97) when the 15 reconstructed time series with the smallest skewness values below 1.2 are omitted (see circled values in Figure 3).

^{0.3}(R

^{2}= 0.90; the linear trendline, i.e., K = 0.6 S + 1.7, achieves a higher R

^{2}= 0.93, but may not be considered physically consistent). Again, the aggregated reconstructed time series are expected to deviate from the rest of the data cloud and approach Gaussianity.

^{2}, where n = 365 × 24 × 6 is approximately the total number of 10 min in one year.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The reconstructed streamflow time series at Sacramento from 901 to 1977 (in 10× hm

^{3}/year and of annual resolution), the reconstructed streamflow time series from the Missouri database from 1473 to 2005 (with ID 6278300, in 10

^{−2}× hm

^{3}/year and of annual resolution) and the 6th streamflow recorded time series from the Swiss database ranging from 1974 to 2017 (in hm

^{3}/year and of aggregated monthly resolution).

**Figure 2.**Mean vs. standard deviation of streamflow time series from the analysis by Dimitriadis et al. [6] (daily and hourly time series, denoted as Global), for the Swiss dataset (10 min resolution, denoted as Swiss) and for the paleoclimatic reconstructions (annual time series, denoted as Paleo. Rec.).

**Figure 3.**Skewness coefficient vs. kurtosis coefficient of the streamflow time series from the Dimitriadis et al. [6] analysis (daily and hourly time series, denoted as Global), for the Swiss dataset (10 min resolution, denoted as Swiss) and for the paleoclimatic reconstructions (annual time series, denoted as Paleo. Rec.).

**Figure 4.**K-skewness vs. K-kurtosis of streamflow time series from the analysis by Dimitriadis et al. [6] (daily and hourly resolution, denoted as Global), for the Swiss dataset (10 min resolution, denoted as Swiss), and for the paleoclimatic reconstructions (annual resolution, denoted as Paleo. Rec.).

**Figure 5.**The mean standardized climacogram for the analysis by Dimitriadis et al. [6] (daily and hourly resolution), for the Swiss dataset (10 min resolution) and for the paleoclimatic reconstructions (annual resolution).

**Figure 6.**The mean standardized climaco-variogram for the analysis by Dimitriadis et al. [6] (daily and hourly resolution), for the Swiss dataset (10 min resolution) and for the paleoclimatic reconstructions (annual resolution).

**Figure 7.**The mean standardized CBS for the analysis by Dimitriadis et al. [6] (daily and hourly resolution), for the Swiss dataset (10 min resolution) and for the paleoclimatic reconstructions (annual resolution).

Number of Stations | Temporal Resolution | Total Record Values/Station | Time Period | Location | Type | Database | |
---|---|---|---|---|---|---|---|

Swiss dataset | 39 | 10 min | 2.3 × 10^{6} | 1974–2017 | Switzerland | Stations | Hyperlink |

Missouri paleoclimatic reconstruction dataset | 55 | Annual | 533 | 1473–2005 | Missouri river basin, USA | Reconstructions | Hyperlink |

Sacramento reconstruction timeseries | 1 | Annual | 1077 | 901–1977 | Sacramento River, USA | Reconstruction | Hyperlink |

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**MDPI and ACS Style**

Pizarro, A.; Dimitriadis, P.; Iliopoulou, T.; Manfreda, S.; Koutsoyiannis, D. Stochastic Analysis of the Marginal and Dependence Structure of Streamflows: From Fine-Scale Records to Multi-Centennial Paleoclimatic Reconstructions. *Hydrology* **2022**, *9*, 126.
https://doi.org/10.3390/hydrology9070126

**AMA Style**

Pizarro A, Dimitriadis P, Iliopoulou T, Manfreda S, Koutsoyiannis D. Stochastic Analysis of the Marginal and Dependence Structure of Streamflows: From Fine-Scale Records to Multi-Centennial Paleoclimatic Reconstructions. *Hydrology*. 2022; 9(7):126.
https://doi.org/10.3390/hydrology9070126

**Chicago/Turabian Style**

Pizarro, Alonso, Panayiotis Dimitriadis, Theano Iliopoulou, Salvatore Manfreda, and Demetris Koutsoyiannis. 2022. "Stochastic Analysis of the Marginal and Dependence Structure of Streamflows: From Fine-Scale Records to Multi-Centennial Paleoclimatic Reconstructions" *Hydrology* 9, no. 7: 126.
https://doi.org/10.3390/hydrology9070126