Karst#

[text here]

Introduction#

Methods#

## 2.1 Collating Ground-Based GWR Estimates

Ground-based GWR estimates from hundreds of published studies and databases were compiled into a single global dataset. Each estimate was:

  • Mapped to a 0.5° × 0.5° grid cell (same as WaterGAP resolution).

  • Standardized in units and reference period to ensure comparability.

  • Filtered to remove duplicates, outliers, and short-term measurements.

The result is a harmonized benchmark dataset of grid-cell GWR used for tuning and validation.

—

## 2.2 Simulating GWR With WaterGAP 2.2e

### Overview

WaterGAP partitions effective precipitation into runoff components and then computes diffuse groundwater recharge (GWR) as a capped fraction of one component.

### Step 1 — Partition Effective Precipitation

  1. Urban runoff R₁: 50% of effective precipitation on urban land is direct runoff.

  2. Soil overflow R₂: Excess water when soil storage exceeds capacity.

  3. Nonlinear runoff R₃ (Eq. 1):

[ R_3 = P_{text{eff}} left(frac{S_s}{S_{s,max}}right)^{gamma} ]

where (S_s) is current soil water storage, (S_{s,max}) its maximum capacity, and (gamma) a calibrated exponent.

### Step 2 — Compute Diffuse Recharge (Eqs. 2 & 3)

[ R_g = min(R_{g,max}, f_g cdot R_3) ]

where (f_g) is the product of four modifiers:

[ f_g = f_r cdot f_t cdot f_h cdot f_{pg} ]

  • f_r: relief/slope factor

  • f_t: soil texture factor

  • f_h: hydrogeology factor

  • f_pg: permafrost/glacier factor

Daily maximum recharge (R_{g,max}) is capped by soil type (coarse: 7 mm/d, medium: 4.5 mm/d, fine: 2.5 mm/d).

### Step 3 — Groundwater Storage

Recharge is added to a groundwater store and released to rivers as baseflow:

[ Q_{gw to sw} = k cdot S_{gw} ]

where (k) is the groundwater discharge coefficient and (S_{gw}) groundwater storage.

—

## 2.3 Simulating GWR in Karst

### Localization of Karst Areas

Karst is identified using the World Karst Aquifer Map (WOKAM). The karst fraction of each grid cell is computed as (Eq. 4):

[ f_{text{karst}} = min left(f_{k,max}, frac{sum_i text{Share}_i A_{text{overlay},i}}{A_{text{cont}}}right) ]

where shares are 0.4 for discontinuous and 0.9 for continuous/mixed categories, capped at (f_{k,max}=0.9).

### Karst GWR Calculation

For karst cells, recharge is simply:

[ R_{g,text{karst}} = R_3 ]

### Combine Karst and Non-Karst Recharge (Eq. 8)

[ R_{g,text{grid}} = frac{f_{text{karst,land}}}{f_{text{land}}} R_{g,text{karst}} + left(1 - frac{f_{text{karst,land}}}{f_{text{land}}}right) R_g ]

This weights karst recharge and diffuse recharge by their respective land fractions.

—

## 2.4 Modifying the Computation of GWR Outside of Karst Areas

### Data Updates

  • Relief factor: recalculated using modern global DEMs.

  • Soil factor: updated from Harmonized World Soil Database.

### Revised Recharge Cap (Eq. 7)

[ R_{g,max} = begin{cases} 7.0 & text{coarse soils} \ 4.5 & text{medium soils} \ 2.5 & text{fine soils} end{cases} ]

Recharge in semi-arid coarse soils is only generated when precipitation exceeds 12.5 mm/d.

### Regional Adjustments

  • Removed Mississippi Embayment correction (no longer needed).

  • Removed Bangladesh wetland mask (allowed recharge).

### Calibration

Parameters (f_r, f_t) were tuned against the global GWR dataset, minimizing bias and RMSE while preserving streamflow match.

—

## 2.5 Parameter Tuning Procedure

A global optimization approach was applied:

  1. Run baseline simulation with initial parameters.

  2. Compute error between simulated and observed GWR.

  3. Adjust (f_r, f_t, f_h, f_{pg}, k) within plausible ranges.

  4. Re-simulate, recalculate error, iterate until convergence.

Performance was measured using RMSE, bias, and fit to streamflow signatures.

—

## 2.6 Validation

After tuning, model results were validated against:

  • Independent GWR data not used in calibration.

  • Streamflow observations from GRDC stations.

This ensured that improved recharge estimation did not degrade river discharge performance.

—

## 2.7 Impact Analysis

Finally, the impact of the methodological improvements was analyzed:

  • Global mean GWR: compared to previous WaterGAP versions.

  • Spatial distribution: mapped to assess regional differences.

  • Contribution of karst: quantified as percentage of global recharge.

  • Streamflow fit: checked to ensure good agreement with observed hydrographs.

—

Summary: Chapter 2 describes how WaterGAP 2.2e was enhanced by explicitly simulating karst recharge, updating input data for non-karst regions, tuning parameters to a large global dataset, and validating results against observations. These steps yield more reliable global GWR estimates and improve agreement with both point measurements and streamflow records.

On this page

This Page