Update weighted ensemble example

Use newly implemented cap to bias correction offsets.

Author: ConnectedSystems

docs/src/assets/ensemble_bias_corrected.png

@@ -86,7 +86,7 @@ low flows as with GR4J.
 
 ![](../../assets/ensemble_model_comparison_quickplots.png)
 
-Comparing the temporal cross section:
+Comparing the temporal cross section to get an idea of seasonality:
 
 ```julia
 ihacres_xs = temporal_cross_section(burn_dates, burn_obs, ihacres_node.outflow[burn_in:end]; title="IHACRES", yscale=:log10)
@@ -101,10 +101,11 @@ A reduction in the median error can be seen with extreme errors reduced somewhat
 ![](../../assets/ensemble_xsection.png)
 
 The median error can then be applied to modelled streamflow (on a month-day basis) as a
-form of bias correction.
+form of bias correction. Here, the correction factor is capped to -80% and +40% of predicted
+outflows.
 
 ```julia
-q_star = Streamfall.apply_temporal_correction(ensemble, climate, Qo[:, "410730"])
+q_star = Streamfall.apply_temporal_correction(ensemble, climate, Qo[:, "410730"]; low_cap=0.8, high_cap=0.4)
 
 bc_ensemble_qp = quickplot(burn_obs, q_star[burn_in:end], climate; label="Bias Corrected Ensemble", log=true)
 
@@ -116,16 +117,17 @@ bias_corrected_xs = temporal_cross_section(
     yscale=:log10
 )
 
-plot(bc_ensemble_qp, bias_corrected_xs; layout=(2,1), size=(800, 800))
+ens_qp = plot(bc_ensemble_qp, bias_corrected_xs; layout=(2,1), size=(800, 800))
 ```
 
-While the median error has increased, its variance has reduced significantly. At the same
-time, performance at the 75 and 95% CI remain steady relative to the original weighted
-ensemble results.
+It can be seen here that low flows are better represented, with a commensurate decrease
+in median error (and its variance). At the same time, performance at the 75 and 95% CI 
+remain steady relative to the original weighted ensemble results.
 
 ![](../../assets/ensemble_bias_corrected.png)
 
 This ensemble approach may be improved further by:
 
 - Using a rolling window to smooth ensemble predictions
 - Defining a custom objective function to target specific conditions
+- Using more advanced ensemble approaches other than the simple weighted mean approach

docs/src/assets/ensemble_model_comparison_quickplots.png

@@ -1,4 +1,4 @@
-import ..Analysis: TemporalCrossSection
+import ..Analysis: TemporalCrossSection, offsets
 
 Base.@kwdef mutable struct WeightedEnsembleNode{N<:NetworkNode,P,A<:Real} <: EnsembleNode
     name::String
@@ -177,20 +177,31 @@ end
     apply_temporal_correction(
         ensemble::WeightedEnsembleNode,
         climate::Climate,
-        obs::Vector{T}
+        obs::Vector{T};
+        low_cap::Float64=1.0,
+        high_cap::Float64=1.0
     ) where {T<:Real}
 
 Correct for model bias using median error.
+By default, the correction is capped to ± 100% of model prediction modified by
+`low_cap` and `high_cap`
 """
 function apply_temporal_correction(
     ensemble::WeightedEnsembleNode,
     climate::Climate,
-    obs::Vector{T}
-) where {T<:Real}
+    obs::Vector{Float64};
+    low_cap::Float64=1.0,
+    high_cap::Float64=1.0
+)
+    low_cap = clamp(low_cap, 0.0, 1.0)
+    high_cap = clamp(high_cap, 0.0, 1.0)
+
     dates = timesteps(climate)
     tcs = TemporalCrossSection(dates, obs, ensemble.outflow)
 
-    return max.(ensemble.outflow .+ Streamfall.Analysis.offsets(tcs), 0.0)
+    x = min.(ensemble.outflow .+ offsets(tcs), ensemble.outflow .* (1.0 + high_cap))
+
+    return max.(x, ensemble.outflow .* (1.0 - low_cap))
 end
 
 """