.. _karst:

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Karst
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[text here]

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Introduction
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Methods
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## 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.