small changes

Author: MarkMelotto

book/thesis_projects/BSc/2025_Q3_IschaHollemans_CEG/Report/3_historical_droughts.md

@@ -27,18 +27,19 @@ date where the discharge falls below the critical water flow of 66.5 m³/s. This
 and thus the beginning of a deficit. For each day onward, the algorithm calculates the difference
 between current discharge and the critical flow:
 
-$$D(t) = (Q(t) - Q_{crit})$$
+$$ D(t) = (Q(t) - Q_{crit}) $$
 
 If the value is negative, it stands for deficit. If the value is positive, it means that the hydrological system
 gets replenished. The severity of the deficit is quantified by taking the maximum cumulative water deficit
 which uses the following formula:
-$$D_{cum}(t) = \sum_{i=0}^{t} D(i)$$
+$$ D_{cum}(t) = \sum_{i=0}^{t} D(i) $$
 
 By using this for every timestep, the following list is created equation 3. The maximum cumulative deficit
 is eventually calculated using equation 4.
 
-$$D_{cum,list} = \left[ D_{cum}(1),D_{cum}(2), ..., D_{cum}(n) \right]$$
-$$D_{max} = \text{max} \left( |D_{cum,list(t)}| \right) \text{,   } t \in [1,n]$$
+$$ D_{cum,list} = \left[ D_{cum}(1),D_{cum}(2), ..., D_{cum}(n) \right] $$
+
+$$ D_{max} = \text{max} \left( |D_{cum,list(t)}| \right) \text{,   } t \in [1,n] $$
 
 The drought period is defined by the amount of time it takes for the system to replenish the amount of
 lost water. In figure 3, a visualisation of the length of a drought $T_{drought}$, and $D_{max}$ is displayed:

book/thesis_projects/BSc/2025_Q3_IschaHollemans_CEG/Report/4_future_droughts.md

@@ -45,8 +45,10 @@ duration and deficit.
 These cumulative distributions are then used for quantifying the difference between historical and future
 droughts in terms of return period. This is achieved by using the drought return period function used by
 Zhao, et al. (2017):
-$$T_D = \frac{N}{n\left( 1-F_D(d) \right)}$$
-$$T_S = \frac{N}{n\left( 1-F_S(s) \right)}$$
+
+$$ T_D = \frac{N}{n\left( 1-F_D(d) \right)} $$
+
+$$ T_S = \frac{N}{n\left( 1-F_S(s) \right)} $$
 
 The return period for duration is defined by $T_D$, and for severity (deficit) $T_S$. The length of the dataset is
 expressed by $N$, which is equal to 72 years. The number of drought observations is denoted by $n$. The
@@ -55,7 +57,7 @@ duration and $F_S(s)$ for drought severity (deficit).
 To make sure that the modelled return periods are precise, the historical CMIP6 droughts are validated
 using the observed past droughts. The validation is displayed in figure 10:
 
-!figure10](figures/figure10.png)
+![figure10](figures/figure10.png)
 *Figure 10: Validation of the return periods for 1942-2014. The graphs show a significant discrepancy for
 both drought duration and deficit.*
 

book/thesis_projects/BSc/2025_Q3_IschaHollemans_CEG/ischa/CMIP_Future_prediction.ipynb

@@ -5,7 +5,7 @@
    "id": "4839d59f-30b4-47b8-bbdd-694bbcf458cf",
    "metadata": {},
    "source": [
-    "# CMIP Future prediction\n",
+    "# Generating (CMIP6) future droughts\n",
     "\n",
     "This notebook is used to predict future discharge values for the Loire river at Blois. For these prediction, different climate scenarios are used: SSP126, SSP2455 and SSP585. These discharge values are then analysed using the drought analyser (Drought_analyser.ipynb) to assess the difference between past and future. "
    ]