# High-Performance Forecasting of Spring Flood in Mountain River Basins with Complex Landscape Structure

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Database

^{2}).

^{3}/s. We supplemented runoff observations with the values of monthly precipitation and average monthly air temperatures, the GIS information (Institute for Water and Environmental Problems SB RAS, Barnaul, Russia) on landscape structure of the territory, the area, and altitude of landscapes in each river basin.

^{3}/s to dimensionless units, we created a single homogeneous sample of runoffs for all rivers over the 70-year period 1951–2020. Landscape areas (km

^{2}) in each basin were also converted to shares/percentages via dividing by each basin area.

#### 2.2. Methodology of System-Analytical Modeling

^{2}= 1 − 2A

^{2}.

#### 2.3. Advantages of System-Analytical Modeling

- The identification of typological groups of geosystems (13 types of landscapes in Table 1) as autonomous hydrological subsystems of river basins with regard for their altitude belt and structural-tier heterogeneity, which is based on ArcGIS processing of cartographic materials of scale 1:200,000 [25];
- The normalization and spatial generalization of average monthly air temperatures and monthly precipitation for the mountainous areas according to the data from rare reference weather stations [26,27]. As a result, the orographic characteristics of river basins have practically no effect on the long-term dynamics of these factors and normalized river runoffs [33]. It should be noted that the reanalysis data for the Altai-Sayan mountain country are hardly suitable for building high-performance runoff models because of a sparse network of weather stations (11 reference weather stations involved in our study are located on the territory of 2,000,000 km
^{2}) and change in precipitation up to an order of magnitude with variations in altitude [29]; - The application of free-form function H (Figure 4) able to adapt to real dependence of process on environmental factors. On the contrary, fixed forms of equations usually prevent models of complex natural systems from best performance.

## 3. Results

_{k}, b

_{k}—the parameters characterizing k-th landscape contributions to river runoff for the relevant period (Table 2), k = 1–13; ${S}_{k}^{i}$—the relative area of k-th landscape of basin i; ${h}_{k}^{i}$—the landscape elevation, m a.s.l.; P

_{1}, P

_{2}—the mean deviations of normalized monthly precipitation from 1 (value 1 is the long-term average of normalized factor) in recent autumn and current winter periods, respectively; T

_{2}—the mean deviation of normalized monthly air temperature from 1 in the current winter period; H—the piecewise–linear function (1); ${c}_{1\u20134}$, ${c}_{5\u20138}$, ${c}_{9\u201312}$—the parameters describing the influence of autumn precipitation P

_{1}and winter temperature T

_{2}on runoff volume in April as well as landscape elevation ${h}_{k}^{i}$ on precipitation amount; and d—the constant fraction of normalized runoff (d ≤ 1) equal for all river basins, which depends on flow loss into soils and fractured rock zones.

_{1}(soaked the soils going into winter) of the previous autumn, as well as ${S}_{k}^{i}$ and ${h}_{k}^{i}$ of landscapes. In the second summand in (4), landscape contributions are provided by winter precipitation P

_{2}and depend on ${S}_{k}^{i}$, ${h}_{k}^{i}$, autumn precipitation P

_{1}, and winter temperature T

_{2}, which affects moisture evaporation from the snow cover surface. Multiplier $H({c}_{1},{c}_{2},1,1,{c}_{3},{c}_{4},{P}_{1})$ in (4) accounts for moisture exchange between soils and snow cover in winter depending on soil moistening by autumn precipitation P

_{1}[37].

_{2}and landscape altitude ${h}_{k}^{i}$ have the least effect on flood. The situation with T

_{2}is explained by the fact that incoming solar radiation, not air temperature, is responsible for most heat consumption needed for snow melting. The minimal altitude influence confirms adequate description of dynamics of meteorological factors via their normalized values. The latter hardly depend on the terrain altitude [30], while the altitude dependence of temperatures (in °C) and precipitation (in mm) is great [29,39].

## 4. Analysis of Results and Discussion

_{2}> 0, fall in winter air temperature T

_{2}< 0 results in lower temperature of thick snow cover, greater storage, and longer time lags for spring meltwater to travel through a snowpack [40] and move downslope into rivers. These processes bring to reduction in April runoff Q. With growing T

_{2}> 0, Q drops again due to slower freezing of soils and more intensive moisture transition to lower soil layers and groundwater [41], resulting in soil insiccation in winter and greater loss of meltwater for soil soaking in spring.

_{2}< 0, April runoff Q grows with air temperature drop T

_{2}< 0 in winter (Figure 5b). A thin snow cover contributes to the deep freezing of soils in winter (up to 2–3 m [37]). In spring, such a freeze facilitates ice layer formation in the upper soil layer and prevents meltwater infiltration into soil [37]. The lower the T

_{2}, the larger the area of the ice layer is and the more meltwater come into rivers. Rise in temperature T

_{2}> 0 also results in increased runoff Q caused by more intensive melting of snow cover on slightly frozen soils at all altitudes. Such an increase in runoff Q is limited by incoming solar radiation responsible for 50–80% of snowmelt and runoff formation [42].

_{0}. To find it, we evaluate the components of the residual variance ${\left({S}_{\mathrm{dif}}\right)}^{2}$ for the model (4) through the method of model uncertainty quantification [33]. In accordance with the method, ${\left({S}_{\mathrm{dif}}\right)}^{2}$ adds up the variance components formed by equation inaccuracy, observation errors of input factors and output variable, and unaccounted variations of input factors (blurring of landscape structure in our case) [30,33]. In ${\left({S}_{\mathrm{dif}}\right)}^{2}$, we can select the components, which are absent in residual variance of the model (5), and estimate the remaining component that characterizes A

_{0}. Given (2) and (3), we get:

_{L}is the contribution from unaccounted variations in landscape hydrological characteristics a

_{k}and b

_{k}(Table 2 and Table 3), FS

_{P}, FS

_{T}are the contributions from precipitation variations and air temperature variations (Table 3), $2{A}_{P}^{2}$, $2{A}_{T}^{2}$ are the shares in variances of precipitation and air temperature variations, which are formed by errors of their spatial averaging, A

_{P}, A

_{T}are the adequacy (2) for spatial averaging of the same meteorological factors, and $2{A}_{0}^{2}$ is the sought component of ${\left({S}_{\mathrm{dif}}\right)}^{2}$ characterizing adequacy A

_{0}of Equation (5).

_{L}= 0.49, FS

_{P}= 0.14, FS

_{T}= 0.007 (Table 3), and averages A

_{P}= 0.73 and A

_{T}= 0.32 for autumn (IX–XI) and/or winter (XII–III) months [26], we obtain A

_{0}for the model (5) describing an individual river basin:

_{0}≈ 0.34 characterizes adequacy of April monthly flood forecasts for any river basin of the Altai-Sayan mountain country. Indeed, a sample of normalized observed runoff from any typical basin and a similar sample of runoff from 34 basins will have the same (differing only in volumes) statistical characteristics. Therefore, A

_{0}values of forecast adequacy in both cases will be the same.

_{0}≈ 0.34, we get a fourfold reduction in variance:

_{0}= 1 − $2{A}_{0}^{2}$ (see notation for Equation (2)). At A

_{0}≈ 0.34, NSE

_{0}≈ 1 − 2(0.34)

^{2}≈ 0.77. Note that just one mathematical criterion (A, NSE, RSR. R

^{2}, etc.) is sufficient for assessing our process-driven model adequacy [33]. Process-driven models describe real physical–hydrological processes, and consistency between the obtained simulation results and the related scientific concepts serves as an extra confirmation of the model performance. In turn, data-driven models based on statistical techniques for data processing employ two or more different criteria [7,9].

_{0}≈ 0.77 is in the best range (0.75 < NSE ≤ 1.0) for mathematical models [32]. It is important that floods are predicted with such a “very good” quality for the mountain areas, the hydrological processes of which are extremely hard to simulate. Moreover, the obtained quality can be improved through application of the established dependence of spring floods on April meteorological conditions [20]. Such refinement of forecasts obtained from (5) is easily performed by substituting the available meteorological prognoses of air temperature and precipitation for April into this dependence.

## 5. Conclusions

- Description of meteorological factors and river runoffs as a fraction of the corresponding long-term averages made it possible to unify their dynamics throughout the Altai-Sayan mountain country. The performed normalization and spatial generalization of average monthly air temperature and monthly precipitation over the entire territory of the country adequately reflect their long-term dynamics and ensure more accurate calculations of hydrological processes in contrast to in situ observations at rare weather stations;
- The developed universal predictive model (4) adequately describes the influence of environmental factors on April monthly runoffs with ice motion for 34 rivers of the Altai-Sayan mountain country. It takes into account the landscape structure (geosystems) of river basins, monthly values of temperature and precipitation for the previous autumn and winter, as well as watershed altitudes. The obtained universal dependences of runoff on meteorological factors correlate with physical–hydrological patterns of snow cover melting, freezing and thawing of moistened soil (depending on snow cover thickness), ice layer formation in the upper soil layer (preventing meltwater infiltration into soil), and solar radiation effect. The reverse transition from normalized river runoffs in (4), (5) to their measurement in m
^{3}/s is easily performed through multiplication by the corresponding long-term average runoff of the basin. Our findings expand the existing notion about hydrological processes and factors, which determine the intensity of annual spring floods in the mountains; - The sensitivity of the developed model (April monthly runoff with ice motion) to natural variations in temperature and precipitation, landscape structure of river basins, and landscape altitude was estimated. In contrast to other methods for assessing model sensitivity, our methodology excludes the influence of observation errors of environmental factors. Using the method of model uncertainty quantification aimed at the estimation of all residual variance components, we evaluated the performance of a simplified version of the developed model applicable to any river basin;
- The simplified model (5) provides a medium-term April flood forecast for any river basin in the Altai-Sayan mountain country or other mountainous areas. The forecast quality is characterized by the Nash–Sutcliff coefficient NSE
_{0}≈ 0.77 that is “very good” for hydrological models of mountain rivers. The value of NSE_{0}can be further improved by means of additional consideration of standard meteorological prognoses of air temperature and precipitation for April. In the country under study, April runoffs turn occasionally into catastrophic floods [23]. Timeliness and high accuracy of forecasts are extremely important for decision making in ensuring local population safety and for the region administration provided with flood forecasts performed according to the developed methodology; - The proposed SAM methodology of building the process-driven hydrological (and hydrochemical) models provides an in-depth study of complex hydrological systems with a lack of information on their structure and functional relationships with environmental factors. Thus, this methodology can serve as an effective scientific tool for studying natural hydrological systems influenced by environmental and anthropogenic factors.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Map scheme of the location of 34 model river basins of the Altai-Sayan mountain country [24].

**Figure 2.**In the mountains, snow, rain, and zero precipitation may occur concurrently at different altitudes (the photo by unknown author shows the Shavla River basin in the Altai Mountains).

**Figure 4.**Continuous function H(X1,X2,Y1,Y2,Z1,Z2,X) consisting of three linear fragments with arbitrarily changing parameters in Equation (1) [24].

**Figure 5.**Dependence of April monthly floods (with ice motion) of the river Katun on air temperature and precipitation for preceding seasons (we show deviations of normalized monthly meteorological characteristics from their long-term averages, see notation for Equation (4)). (

**a**) April runoff Q as a function of precipitation P

_{1}(IX–XI) and P

_{2}(XII–III); (

**b**) April runoff Q as a function of temperature T

_{2}(XII–III) and precipitation P

_{2}.

**Table 1.**Identified types of landscapes of the Altai-Sayan mountain country [25].

Landscapes (Geosystem Groups) |
---|

1. Glacial–nival high mountains with permafrost |

2. Goletz alpine-type high and middle mountains, pseudogoletz low mountains with permafrost |

3. Tundra–steppe and cryophyte–steppe high mountains with permafrost |

4. Forest high middle and low mountains |

5. Exposure foreststeppe and steppe high and middle mountains |

6. Forest–steppe, steppe low mountains and foothills |

7. Intermountain depressions with different steppes and forest–steppes |

8. Steppe and forest–steppe piedmont |

9. Nondrainable and intrazonal landscapes with partial permafrost |

10. Mountain river valleys |

11. Lowland river valleys |

12. Forest high and piedmont plains |

13. Aquatic landscapes |

**Table 2.**Contributions of landscapes to April monthly flood on rivers of the Altai-Sayan mountain country.

Landscapes (Geosystem Groups) | Contributions (a _{i}, b_{i} in Equation (4)) | |
---|---|---|

a | b | |

1. Glacial–nival high mountains with permafrost | 0.06 | 0 |

2. Goletz alpine-type high and middle mountains, pseudogoletz low mountains with permafrost | 0.12 | 0.08 |

3. Tundra–steppe and cryophyte–steppe high mountains with permafrost | 0.07 | 0 |

4. Forest high middle and low mountains | 0.41 | 0.56 |

5. Exposure forest–steppe and steppe high and middle mountains | 0.39 | 0.55 |

6. Forest–steppe, steppe low mountains and foothills | 0.73 | 0.17 |

7. Intermountain depressions with different steppes and forest–steppes | 0 | 0.07 |

8. Steppe and forest–steppe piedmont | 0.79 | 0 |

9. Nondrainable and intrazonal landscapes with partial permafrost | 3.55 | 0 |

10. Mountain river valleys | 0.23 | ~0 |

11. Lowland river valleys | 1.65 | 1.05 |

12. Forest high and piedmont plains | 0.66 | 0 |

13. Aquatic landscapes | 0 | 0 |

Characteristic | Value |
---|---|

Adequacy A of model (4) according to Equation (2) | 0.66 |

Standard deviation ^{2} S_{obs} of actual river runoff Q | 0.44 |

Sensitivity FS_{L} to variations in landscape structure of river basins ^{3} | 49 |

Sensitivity FS_{P} to joint variations in autumn and winter precipitation (P_{1} and P_{2}) | 14 |

Sensitivity FS_{P}_{1} to autumn precipitation P_{1} | 9 |

Sensitivity FS_{P}_{2} to winter precipitation P_{2} | 3 |

Sensitivity FS_{T} to winter air temperature T_{2} | 0.7 |

Sensitivity FS_{h} to landscape elevation ${h}_{k}^{i}$ | <0.1 |

^{1}estimated by (3) and expressed in percent of variance (S

_{obs})

^{2};

^{2}calculated as mean standard deviation of normalized observed runoff in 34 river basins. At the same time, it corresponds to mean standard deviation in fractions (or as percentage when multiplied by 100%) of non-normalized observed runoff; and

^{3}calculated via joint random mixing values of landscape hydrological characteristics (a

_{k}and b

_{k}in (4)) among 34 basins, k = 1–12.

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**MDPI and ACS Style**

Kirsta, Y.B.; Troshkova, I.A.
High-Performance Forecasting of Spring Flood in Mountain River Basins with Complex Landscape Structure. *Water* **2023**, *15*, 1080.
https://doi.org/10.3390/w15061080

**AMA Style**

Kirsta YB, Troshkova IA.
High-Performance Forecasting of Spring Flood in Mountain River Basins with Complex Landscape Structure. *Water*. 2023; 15(6):1080.
https://doi.org/10.3390/w15061080

**Chicago/Turabian Style**

Kirsta, Yuri B., and Irina A. Troshkova.
2023. "High-Performance Forecasting of Spring Flood in Mountain River Basins with Complex Landscape Structure" *Water* 15, no. 6: 1080.
https://doi.org/10.3390/w15061080