AHG/FHG Data

Using the USGS “HYDRoacoustic dataset in support of the Surface Water Oceanographic Topography satellite” mission (HYDRoSWOT) Johnson et al., 2023 provided a robust dataset of fitted AHG parameters, that uses the best combination of linear, nonlinear least square fits, and a constrained genetic algorithm. We use the derived FHG coefficient and exponents to build a machine learning model to translate catchment and station surrounding surface, subsurface, climate and anthropogenic characteristics into FHG coefficient and exponents. This coefficients would represent in channel geometrical characteristics that can be used to inform hydrological models and enhance flood mapping.

this done by considering the continuity relations that can be derived from the above power-law forms

In-channel shape

Dingman (2007) derived a symmetrical channel cross section as

where z is height of the bed at the lowest channel elevation point, x is horizontal distance from the center, ΨBF is the bankfull maximum depth, and WBF is bankfull width. The exponent r reflects the cross-section shape: 

We can plot the distribution of predictor variables from reference fabric attributes dataset. These values are power transformed and standardized. The three colors represent a low, mid, and high classification of values of corresponding exponent coefficient. The two thresholds are derived from 33 and 66 quantiles of exponent coefficient values.

Here we implement different machine learning approaches to model 6 FHG coefficients using different datasets 

This dataset is comprised of upstream drainage area characteristics 

• Definitions 

1.  hwnodesqkm --> Area that drains to the headwater node in square kilometers <font color='red'>contains NaN!</font> 

2.  slopelenkm --> Flow-line length used to calculate slope, in kilometers 

3.  slope --> Slope of the flowline from smoothed elevation (unitless) 

4.  streamorde --> Modified Strahler stream order

5.  streamleve --> Stream level 

6.  totdasqkm --> Total cumulative area, in square kilometers 

7.  pathlength --> Distance downstream to network end 

8.  arbolatesu --> Arbolate sum, the sum of the lengths of all digitized flowlines upstream from the downstream end of the immediate flowline, in kilometers

9.  areasqkm --> Catchment area, in square kilometers 

10. lengthkm --> From NHDFlowline feature

11. roughness --> Manning's roughness

During data preprocessing,  due to NaN values in hwnodesqkm parmeter a dummy variable is introduced "hwnodesqkm_dummy" and NaN varibles are converted to 0 

The POLARIS soil dataset is comprised of the following features:

• Definitions 

1.  alpha_mean_0_5 --> parameter of the van Genuchten equation corresponding approximately to the inverse of

the air-entry value, (cm-1) 

2.  bd_mean_0_5 --> the soil bulk density, (g cm-3)

3.  clay_mean_0_5 --> % clay 

4.  hb_mean_0_5 --> Brooks-Corey parameter related to the air-entry  pressure (cm)  

5.  ksat_mean_0_5 --> the effective saturated hydraulic conductivity, (cm hr-1) 

6.  lambda_mean_0_5 --> Brooks-Corey parameter the pore size distribution index, (dimensionless)

7.  n_mean_0_5 --> the empirical shape-defining parameters in the van Genuchten equation, (dimensionless) 

8. om_mean_0_5 --> the organic matter content, (%)

9. ph_mean_0_5 --> soil PH 

10. sand_mean_0_5 --> % sand 

11.  silt_mean_0_5 --> % silt 

12. theta_r_mean_0_5 --> the residual soil water content, (cm3 cm-3) 

13.  theta_s_mean_0_5 --> the saturated soil water content, (cm3 cm-3) 

14. During data preprocessing,  due to NaN values in some costal areas soil parameter a dummy variable is introduced and NaN variables are converted to 0 

We extract point, buffer and catchment elevation characteristics form DEM dataset:

• Definitions 

1. elevation --> elevation (m) 

2.  aspect--> aspect

3.  slope --> slope 

The EPA streamCat dataset has over 600 metrics that include local catchment (Cat), watershed (Ws), and special metrics and are available for ~2.65 million streams. 

• This dataset contains climate, landsurface, subsurface and anthropogenic variables

We also extracted different characteristics by spatially and temporally aggregating data over the entire period within a buffer of 500m around each station.

• Definitions 

1.  SM_ave --> average Soil moisture (0 - 10 cm underground) m^3 m-3 (source: FLDAS)

2.  SM_max --> maximum Soil moisture (0 - 10 cm underground) m^3 m-3 (source: FLDAS)

3.  SM_min --> minimum Soil moisture (0 - 10 cm underground) m^3 m-3 (source: FLDAS)

4. ST_ave --> average  Soil temperature (0 - 10 cm underground) K (source: FLDAS)

5.  ST_max --> maximum Soil temperature (0 - 10 cm underground) K (source: FLDAS)

6. ST_min --> minimum Soil temperature (0 - 10 cm underground) K (source: FLDAS)

7.  Q_mean --> average  Storm surface runoff kg m-2 s-1 (source: FLDAS)

8. Q_max --> maximum Storm surface runoff kg m-2 s-1 (source: FLDAS)

9. Q_min --> minimum Storm surface runoff kg m-2 s-1 (source: FLDAS)

10. Qb_mean --> average Baseflow-groundwater runoff kg m-2 s-1 (source: FLDAS)

11. Qb_max --> maximum Baseflow-groundwater runoff kg m-2 s-1 (source: FLDAS)

12. Qb_min --> minimum Baseflow-groundwater runoff kg m-2 s-1 (source: FLDAS)

13.  ET_ave --> Total evapotranspiration kg/m^2/8day  (source: MODIS)

14.  AI --> aridity index 

15.  LAI_ave --> average Leaf Area Index (source: MODIS)

16.  LAI_min --> minimum Leaf Area Index (source: MODIS)

17. LAI_max --> maximum Leaf Area Index (source: MODIS)

18. Precip_ave --> average 30-year average of monthly total precipitation (including rain and melted snow) (source: PRISM)

19. Precip_min --> minimum 30-year average of monthly total precipitation (including rain and melted snow) (source: PRISM)

20. Precip_max --> maximum 30-year average of monthly total precipitation (including rain and melted snow) (source: PRISM)

21.  NDVI_ave --> average Normalized difference vegetation index (source: Landsat)

22.  NDVI_min --> minimum Normalized difference vegetation index (source: Landsat)

23. NDVI_max --> maximum Normalized difference vegetation index (source: Landsat)

24.  elevation_ave --> average elevation (source: NASA SRTM Digital Elevation 30m)

25.  slope_ave --> average slope (source: NASA SRTM Digital Elevation 30m)

26. aspect_ave --> median aspect (source: NASA SRTM Digital Elevation 30m)

During data preprocessing,  due to NaN values in hwnodesqkm parmeter a dummy variable is introduced "hwnodesqkm_dummy" and NaN varibles are converted to 0 

Here we use different flow percentiles of national water model (NWM) 2.1 :

• Definitions 

1.  nwm21_min -->  Minimum flow value from NWM2.1

2.  nwm21_25  --> 25% percentiles flow value from NWM2.1

3.  nwm21_50  --> 50% percentiles flow value from NWM2.1

4.  nwm21_75  --> 75% percentiles flow value from NWM2.1

5.  nwm21_max --> Maximum flow value from NWM2.1

We also use different flood frequency values form NWIS:

• Definitions 

6.  ff_1.5 --> 1.5 year flood frequency

7. ff_2  --> 2 year flood frequency

8. ff_5 --> 5 year flood frequency

9. ff_10 --> 10 year flood frequency

10. ff_15 --> 15 year flood frequency

11. ff_25 --> 25 year flood frequency

12. ff_35 --> 35 year flood frequency

13. ff_50 --> 50 year flood frequency

14. ff_60 --> 60 year flood frequency

15. ff_75 --> 75 year flood frequency

16. ff_85 --> 85 year flood frequency

17. ff_90 --> 90 year flood frequency

18. ff_95 --> 95 year flood frequency

19. ff_98 --> 98 year flood frequency

20. ff_99 --> 99 year flood frequency

21. ff_100 --> 100 year flood frequency

22. ff_200 --> 200 year flood frequency

23. ff_500 --> 500 year flood frequency

24. ff_1000 --> 1000 year flood frequency

XGBoost Model 

We used 15% of data for testing, 12.75% for validation and the rest for training purposes.

We implemented a grid search algorithm during the k-fold cross validation to find best hyper parameters using space described below:

'max_depth': [3, 4, 5, 6, 7],

'learning_rate': [0.001, 0.01, 0.05],

'n_estimators': [1000, 2000, 3000, 5000, 6000],

'colsample_bytree': [0.3, 0.5, 0.7]

Each kflod cross validations is repeated 3 times to ensure randomness plays little part in results.

A comprehensive analysis is provided in Importance page

We use three techniques to assess feature Importance:

1- Permutation approach: This approach provides a relative importance scores for the training dataset that is independent of the model used.

2- XGBoost approach: This approach provides a relative importance scores for the training dataset based on the trained XGBoost model that is that provide a deeper insight into feature selection by model.

3-  Shap tree based approach: We use a tree algorithm that is based on game theory and determine XGBoost feature importance's. This also allows us to look at inner interactions between variables.