From hydrological laws to catchment models: A process-based model matches deep-learning accuracy on three continents

Xilin Xia

cs.LGNov 4, 2026

From hydrological laws to catchment models: A process-based model matches deep-learning accuracy on three continents

Authors: Xilin Xia

Organizations: School of Engineering, University of Birmingham, Birmingham, UK

Abstract

Dooge asked whether hydrology has laws at the catchment scale. We ask whether a low-dimensional system built under physical laws can match the accuracy of neural networks that outperform process-based models on the same inputs. Three laws constrain a lumped catchment model. Conservation makes it a flux-connected storage network, dissipation fixes the sign of every flux and aggregation determines how the unresolved composition enters the fluxes, through effective laws over threshold distributions and a memory of the forcing. These laws admit four kinds of refinement. A parsimonious model under them, CaRT (11 parameters per catchment), is refined in a loop assisted by AI agents. Each refinement addresses an observed deficit through a hypothesis from the literature. The result, CaRT+, has fourteen states, 35 parameters per catchment and no daily neural network. Most refinements follow from aggregation over thresholds or from variables that carry no water but modulate fluxes. On 602 British and 593 US gauged catchments, single CaRT+ models reach median Nash-Sutcliffe efficiencies of 0.863 and 0.765 in held-out years. A stateful LSTM reaches 0.869 and 0.751 and an entity-aware LSTM 0.862 and 0.754, while three-seed LSTM ensembles remain ahead of the CaRT+ ensemble by 0.003-0.012 in median paired NSE. On 505 drier Australian gauged catchments unused in development, single CaRT+ models reach 0.778 against 0.762 and 0.753 for the two LSTMs. The results suggest that catchment-scale laws exist as laws of form, with the constitutive families shared and only their parameters learned.

Figures & tables

Statement	Form	Left to assumptions and data
1 Conservation	Storage changes only through fluxes, $\dot{\bm{x}}=\bm{B}\bm{q}+\bm{p}-\bm{e}-\bm{o}+\bm{j}_{\rm ext}$ , ( 1 ). Internal fluxes conserve water, $\bm{1}^{\!\top}\bm{B}=\bm{0}^{\!\top}$ . Every correction acts on a flux.	the number of volumes; the family and parameters of each flux law
2 Dissipation	Potential rises with storage, $\partial H_{i}/\partial x_{i}\geq 0$ . Water flows down the potential, $q_{ij}=L_{ij}\,\Delta H_{ij}$ , $L_{ij}\geq 0$ , ( 2 ). Larger volumes exchange the sum of these fluxes, $q_{IJ}=\sum L_{km}(H_{k}-H_{m})=L_{IJ}\,\Delta H_{IJ}$ , ( 3 ). Phase change is bounded, $E_{a}=E_{\rm dem}\,\varepsilon$ , $0\leq\varepsilon\leq 1$ .	the families of the conductances and of the demand function; their exponents and constants; the lumped potentials, a closure (Law 3)
3 Aggregation	The aggregates obey $\dot{\bm{z}}=\bar{\bm{f}}(\bm{z},\bm{u})+\mathcal{R}$ . The closed law is the mean over the compositions, $\bar{\bm{f}}=\mathrm{E}\big[\bm{\Pi}\bm{f}(\bm{\xi},\bm{u})\,\big\|\,\bm{\Pi}\bm{\xi}=\bm{z},\ \bm{u}\big]$ , ( 7 ). The remainder is a memory of the history, $\mathcal{R}(t)=\mathcal{R}\big[\bm{y}(0);\,\bm{z}\|_{[0,t]},\,\bm{u}\|_{[0,t]}\big]$ , ( 20 ). Only compositions that change the future of $\bm{z}$ need states.	the families of the threshold distribution; the states that carry the memory, by local structure (Table 2 ); the amplitude and time constants of the correction
Corollary: Admissible refinement	(a) Split a volume, $\bm{\Pi}^{\prime}\bm{B}^{\prime}=\bm{B}\bm{K}$ , ( 13 ). (b) Add a connection. (c) Change the form of a flux law. (d) Modulate its coefficients by $\bm{u}$ or $\bm{\chi}$ .	which refinement a catchment needs; the family of each refinement and its parameters

Table 1: The three hydrological laws of this section and their corollary: the form each imposes on a lumped model, and the choices left to constitutive families (assumptions) and parameters (data). The physical basis of each statement is summarised in Section 2.5 .

Local structure	States that carry the memory	Enter the flux as	Size and time scale	Op.
Smooth laws, units in parallel	slow modes of the composition, no water (Eqs. 12 , 21 )	multiplier of a conductance	second order in the heterogeneity of states and properties together; relaxes as the spread drains	d
Smooth laws, units in series	stores for water in transit	convolution of the input (linear laws), or a chain of stores	first order in the rate of change of the input, present for identical units; the travel-time distribution ( 32 )	c, a
Thresholds with a shared driving variable that the stores do not resolve	the driving variable itself, no water	shift or scale of the threshold distribution in ( 8 ), its shape fixed	leading order, through the threshold distribution; the relaxation of the driving variable	d
Units in parallel that fill to a capacity and spill	the current accumulated forcing and its turning points since the last event that filled or emptied all units	shape of the threshold distribution in ( 8 ), which is the deficit distribution	leading order, through the deficit distribution; no time scale, erased by that event	d

Table 2: Memory of the unresolved composition by local structure. The states realise the history functional ( 20 ). Op. is the operation of Corollary 1 through which the memory enters.

Panel of Figure 1 — Figure 1: The structure of CaRT, without the snow store.

Component	Required class	CaRT choice	Parameter
Rain partition	$d=P_{n}\,\eta(s,\dots)$ , $0\leq\eta\leq 1$	$\eta=s^{2}$	$C$
Evaporation	$e_{s}=E_{\rm dem}\,\varepsilon(s,\dots)$ , $0\leq\varepsilon\leq 1$	$\varepsilon=2s-s^{2}$	$C$
Soil drainage	$g=\mathcal{G}(S,W,\dots)$	$g=K_{p}s^{5}$	$K_{p}$
Quick release	$q_{r}=f_{R}(R,\dots)$ , $f_{R}\geq 0$ , $f_{R}^{\prime}\geq 0$	$f_{R}=a_{f}R^{5}$ , $a_{f}=1/(4X_{3}^{4})$	$X_{3}$
Groundwater	$q_{s}=f_{W}(W,\dots)$	$f_{W}=a_{g}W^{2}$ , $a_{g}=1/(\bar{g}\tau^{2})$	$\tau$
Routing	causal, non-negative, unit-mass kernel	UH1/UH2 with scale $X_{4}$	$X_{4}$

Table 3: Components of CaRT: the general class required by Laws 1 – 2 , the choice made and the parameter that controls it. The second column is fixed by the principles, and

f_{R}^{\prime}\geq 0

is assumed. The routing kernel is the travel-time memory of units in series (Section 2.3 ).

Figure 2: The structure of CaRT + .

Refinement	Op.	Fine-scale assumption	Origin	Parameters	Nested limit
Connected fraction of quick release	c, d	connection thresholds, shared depth, wetness converging to a shared value; wetness balance ( 17 )	exact on the slow manifold; logistic shape, shift and balance postulated	$A_{\min}$ , $C_{\theta}$ , $\tau_{\theta}$ , $\lambda$ ; $\theta_{c}$ , $s_{\theta}$ (g)	$A_{\min}\to 1$
Release exponent	c	power-law depth thresholds	asymptotic	$k$	$k=0$
Viscosity	d	conductance $\propto 1/\mu(T)$	physical	none	none (no free parameter)
Frost	d	frozen depth raises thresholds	heuristic	$a_{F}$ ; $T_{F}$ , $s_{F}$ (g)	$a_{F}=0$
Near-stream saturated zone	a, b	small-capacity zone, shallow water table	postulated	$w$ , $C_{z}$ , $\tau_{z}$	$w=0$
Surface layer	a	evaporation at demand, linear drainage	postulated	$C_{u}$ , $\tau_{u}$	$\tau_{u}\to 0$

Table 4: Refinements of CaRT that make up CaRT + . Op.: operation of Corollary 1 . Origin: how the law is obtained, either exact (exact aggregate of a local law under the stated assumption), asymptotic (exact only in a limit), postulated, physical or heuristic (Section 4 ). Parameters are per catchment except where marked global (g).

Figure 3: The refinement loop.

Figure 4: How the laws guide refinement.

	single model									3-seed ensemble
Model	NSE (seeds 0/1/2)	NSE	NSE log	KGE	FHV (%)	FLV (%)	low-flow volume (%)	$n$ (NSE $<$ 0)	NSE ungauged	NSE	NSE log	KGE	NSE ungauged
HBV	0.825 / 0.825 / 0.825	0.825	0.799	0.823	-9.6	-86.9	17.6	7	0.735	0.827	0.808	0.824	0.739
dHBV	0.834 / 0.833 / 0.834	0.832	0.834	0.827	-10.9	-52.6	10.3	14	0.739	0.837	0.844	0.829	0.745
CaRT	0.845 / 0.846 / 0.846	0.845	0.857	0.840	-11.1	-14.0	3.9	5	0.700	0.846	0.860	0.841	0.707
CaRT +	0.864 / 0.864 / 0.862	0.863	0.883	0.856	-10.3	-16.2	7.5	0	0.755	0.866	0.893	0.857	0.766
LSTM	0.871 / 0.870 / 0.867	0.869	0.900	0.871	-7.6	-27.6	6.7	1	0.723	0.879	0.921	0.880	0.737

Table 5: CAMELS-GB, held-out period 2011–2019, medians over the 602 gauged catchments (64 ungauged in the columns so marked). Single model: median NSE of each seed, and medians of the per-catchment metrics averaged over the three seeds; 3-seed ensemble: metrics of the mean simulation.

	single model									3-seed ensemble
Model	NSE (seeds 0/1/2)	NSE	NSE log	KGE	FHV (%)	FLV (%)	low-flow volume (%)	$n$ (NSE $<$ 0)	NSE ungauged	NSE	NSE log	KGE	NSE ungauged
HBV	0.690 / 0.690 / 0.688	0.690	0.447	0.658	-11.6	-88.3	73.2	23	0.632	0.694	0.458	0.660	0.646
dHBV	0.715 / 0.715 / 0.715	0.713	0.591	0.680	-11.0	5.8	59.7	17	0.677	0.719	0.605	0.689	0.681
CaRT	0.723 / 0.724 / 0.725	0.723	0.658	0.726	-9.0	18.4	50.2	24	0.635	0.725	0.661	0.729	0.652
CaRT +	0.760 / 0.768 / 0.765	0.765	0.744	0.784	-6.9	6.7	29.9	21	0.674	0.774	0.767	0.789	0.689
LSTM	0.761 / 0.753 / 0.752	0.751	0.773	0.773	-5.7	-44.1	17.0	17	0.719	0.781	0.817	0.792	0.754

Table 6: CAMELS-US, held-out period 2011–2019, as Table 5 , for 593 gauged basins with at least one year of test data and 68 ungauged.

	single model				3-seed ensemble
Pair	$\Delta$ NSE	$\Delta$ NSE log	$\Delta$ KGE	$\Delta$ NSE ungauged	$\Delta$ NSE	$\Delta$ NSE ungauged
CaRT + $-$ LSTM	$-0.004$ [-0.006, -0.003]	$-0.013$ [-0.015, -0.010]	$-0.014$ [-0.018, -0.012]	$-0.002$ [-0.010, +0.010]	$-0.011$ [-0.012, -0.009]	$-0.004$ [-0.018, +0.008]
CaRT + $-$ EA-LSTM	$+0.001$ [-0.001, +0.002]	$-0.006$ [-0.009, -0.004]	$-0.002$ [-0.005, +0.002]	$+0.004$ [-0.011, +0.020]	$-0.003$ [-0.004, -0.002]	$-0.004$ [-0.019, +0.012]
CaRT + $-$ CaRT	$+0.015$ [+0.013, +0.016]	$+0.023$ [+0.018, +0.027]	$+0.013$ [+0.011, +0.015]	$+0.017$ [+0.003, +0.024]	$+0.016$ [+0.014, +0.017]	$+0.017$ [+0.006, +0.027]
CaRT + $-$ dHBV	$+0.023$ [+0.022, +0.026]	$+0.038$ [+0.033, +0.045]	$+0.029$ [+0.025, +0.033]	$+0.006$ [-0.002, +0.022]	$+0.022$ [+0.021, +0.025]	$+0.015$ [-0.001, +0.031]
CaRT + $-$ HBV	$+0.031$ [+0.028, +0.033]	$+0.078$ [+0.071, +0.083]	$+0.026$ [+0.023, +0.031]	$+0.021$ [+0.007, +0.029]	$+0.032$ [+0.029, +0.034]	$+0.022$ [+0.014, +0.031]

Table 7: Paired per-catchment differences on the held-out period (median and 95 % bootstrap interval). Single model: metrics averaged over the three seeds in each catchment; 3-seed ensemble: NSE of the mean simulation. Top: CAMELS-GB; bottom: CAMELS-US.

Model	BFI $<0.5$	$0.5\leq$ BFI $<0.65$	BFI $\geq 0.65$	$f_{\rm snow}\geq 0.04$
	$n=172$	$n=273$	$n=157$	$n=82$
HBV	0.820 / 0.815 (0.821)	0.839 / 0.814 (0.839)	0.802 / 0.751 (0.805)	0.805 / 0.774 (0.806)
dHBV	0.821 / 0.841 (0.825)	0.849 / 0.849 (0.853)	0.830 / 0.784 (0.837)	0.818 / 0.818 (0.821)
CaRT	0.830 / 0.855 (0.832)	0.859 / 0.866 (0.860)	0.856 / 0.838 (0.859)	0.831 / 0.848 (0.832)
CaRT +	0.847 / 0.877 (0.849)	0.874 / 0.890 (0.876)	0.879 / 0.882 (0.882)	0.847 / 0.863 (0.849)
LSTM	0.845 / 0.888 (0.856)	0.877 / 0.913 (0.887)	0.887 / 0.891 (0.900)	0.845 / 0.877 (0.862)

Table 8: Median single-model NSE / NSE log (per-catchment mean over three seeds) over classes of gauged catchments, held-out period, with the NSE of the three-seed ensemble in parentheses. Top: CAMELS-GB; bottom: CAMELS-US. The classes follow the main hydrological gradient of each sample: the baseflow index on CAMELS-GB, where the permeable chalk and limestone catchments differ most from the rest, and snow fraction and aridity on CAMELS-US.

Dataset	model	ensemble gain	spread on days $\geq Q_{95}$	spread on days $\leq Q_{30}$
CAMELS-GB	CaRT +	$+0.0022$	32 %	6 %
	stateful LSTM	$+0.0093$	57 %	2 %
	EA-LSTM	$+0.0066$	48 %	3 %
CAMELS-US	CaRT +	$+0.0060$	53 %	3 %
	stateful LSTM	$+0.0269$	69 %	1 %
	EA-LSTM	$+0.0163$	62 %	1 %

Table 9: Gain from averaging three seeds on the held-out period: median over gauged catchments of the ensemble NSE minus the mean NSE of the members, which equals the spread of the members relative to the observed variance. Also shown is the share of that spread on the days above the observed 95 % and below the observed 30 % flow quantile.

Figure 5: Scores of the models in the held-out period for the gauged catchments, averaged over three seeds.

Figure 6: NSE of CaRT + on CAMELS-GB in the held-out period and its difference from the other models, with ungauged catchments outlined in black and white areas without test data.

Figure 7: NSE of CaRT + on CAMELS-US in the held-out period and its difference from the other models, with ungauged catchments outlined in black and white areas without test data.

Figure 8: What each group of refinements adds to CaRT + in the held-out period, with medians and 95 % bootstrap intervals.

Group removed from CaRT +	CAMELS-GB	CAMELS-US
Runoff generation (surface layer, Pareto partition, infiltration excess, depression storage, near-stream zone)	$+0.0043$ [+0.0037, +0.0051]	$+0.0054$ [+0.0030, +0.0071]
Quick release (connected release with exponent, viscosity and frost, connected bypass, groundwater-controlled connectivity)	$+0.0058$ [+0.0050, +0.0065]	$+0.0007$ [-0.0007, +0.0013]
Evaporation (vegetation demand, groundwater uptake)	$+0.0010$ [+0.0005, +0.0015]	$+0.0149$ [+0.0126, +0.0178]
Exchange with the exterior (exterior inflow, channel transmission loss)	$+0.0001$ [-0.0004, +0.0003]	$-0.0006$ [-0.0019, +0.0003]
Snow (melt energy term)	$-0.0002$ [-0.0004, -0.0000]	$+0.0002$ [-0.0007, +0.0014]
Sum of the five	$+0.0111$	$+0.0205$

Table 10: Contribution of each group of refinements to CaRT + on the held-out period, their sum and the gain of CaRT + over CaRT. Group contributions are calculated as CaRT + minus CaRT + without the group: paired

\Delta

NSE of the per-catchment mean over three seeds, reported as the median and 95 % bootstrap interval.

Figure 9: Observed and simulated daily flow over one year in six catchments of CAMELS-GB, with the NSE of the whole held-out period in each title.

Figure 10: Observed and simulated daily flow over one year in six catchments of CAMELS-US, with the NSE of the whole held-out period in each title.

Figure 11: NSE of CaRT + against the two LSTMs in the 68 held-out basins of CAMELS-US, with five basins below

-1

placed at the edge.

		median NSE			paired $\Delta$ NSE, CaRT + minus
Class	$n$	CaRT +	LSTM	EA-LSTM	LSTM	EA-LSTM
all held-out basins	68	0.674	0.719	0.722	$-0.003$ [-0.034, +0.020]	$-0.031$ [-0.055, -0.010]
non-arid	46	0.743	0.768	0.773	$+0.002$ [-0.007, +0.025]	$-0.013$ [-0.031, -0.006]
arid (PET/P $>1.1$ )	22	0.256	0.345	0.360	$-0.145$ [-0.319, +0.043]	$-0.112$ [-0.326, -0.053]
snow-dominated, not arid	4	0.867	0.795	0.846	$+0.064$ [-0.172, +0.087]	$+0.020$ [-0.048, +0.041]

Table 11: Held-out basins of CAMELS-US by class (test period, single models: per-basin NSE averaged over three seeds): median NSE and paired differences with 95 % bootstrap intervals.

		held-out catchments			gauged
Dataset	$\sigma$	all	arid (US) / groundwater-fed (GB)	other	all
CAMELS-GB	0 (plain)	0.755	0.428	0.810	0.863
	0.1	0.764	0.435	0.811	0.862
	0.2	0.764	0.449	0.810	0.859
	0.3	0.749	0.500	0.799	0.853
	0.5	0.765	0.593	0.790	0.830

Table 12: Parameter-space ensemble of CaRT + on the held-out period: median NSE over the held-out and the gauged catchments when the standardised attributes of every catchment are perturbed with Gaussian noise of standard deviation

\sigma

and the flows of 32 draws are averaged (per-catchment NSE averaged over three seeds;

\sigma=0

is the single model of the other tables).

Figure 12: NSE of CaRT + on CAMELS-AUS in the held-out period and its difference from the other models, with ungauged catchments outlined in black and white areas without test data.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning	Model	Unit
$N_{k}$ , $k=1..5$	snow water equivalent of band $k$	both	mm (per band area)
$U$	surface layer	CaRT +	mm
$S$	production store (root zone in CaRT + )	both	mm (per area $1-w$ )
$Z$	near-stream saturated zone	CaRT +	mm (per area $w$ )
$V$	depression storage	CaRT +	mm
$H$	water in transit in the unit hydrographs	both	mm

Appendix

Table S1: States of CaRT and CaRT + . Stores carry water and enter the water balance, whereas conditional variables carry none. The fourteen states of CaRT + are the eleven stores other than

H

and the three conditional variables.

H

denotes the water in transit and is listed for the water balance.

Symbol	Meaning (unit)	Range	Map	$p_{0}$
$C$	production-store capacity (mm)	25–1600	log	225
$r_{K}$	percolation scale relative to GR4J, $K_{p}=r_{K}C(4/9)^{4}/4$	1/30–30	log	1
$X_{3}$	quick-store scale (mm); $a_{f}=1/(4X_{3}^{4})$	5–1000	log	33
$X_{4}$	unit-hydrograph time base (d)	0.5–6	lin	1.26
$\tau$	groundwater residence time at $\bar{g}$ (d); $a_{g}=1/(\bar{g}\tau^{2})$	3–1460	log	78
$X_{2}$	exchange (loss) coefficient (mm d -1 ); $j=X_{2}(R/X_{3})^{3.5}$	$-20$ –0	lin	$-0.35$

Appendix

Table S2: Per-catchment parameters of CaRT. Range: open interval of Eq. ( S1 ); map: linear in

p

(lin) or in

\ln p

(log);

p_{0}

: initial value.

Symbol	Meaning (unit)	Range	Map	$p_{0}$	Nested limit
Rain–runoff parameters of CaRT
$C$	root-zone capacity (mm)	25–1600	log	225	–
$r_{K}$	percolation scale relative to GR4J	1/30–30	log	1	–
$X_{3}$	quick-store scale (mm)	5–1000	log	33	–
$X_{4}$	unit-hydrograph time base (d)	0.5–6	lin	1.26	–
$\tau$	groundwater residence time at $\bar{g}$ (d)	3–1460	log	78	–

Appendix

Table S3: Per-catchment parameters of CaRT + (35), with the physical bounds of the main text (

k,a_{F},\lambda,\lambda_{W}\geq 0

). Columns are as in Table S2 , with the last column listing the parameter value at which the refinement vanishes (nested limit). The labels are “open bound” when the limit is the bound of the open interval and “outside” when it lies beyond the range.

Symbol	Meaning	Initial	CAMELS-GB	CAMELS-US	CAMELS-AUS
$T_{F}$	centre of the frost step ( $\mathrm{\SIUnitSymbolCelsius}$ )	0	$-0.28$ to $0.07$	$-0.11$ to $0.07$	$-0.04$ to $-0.03$
$s_{F}$	width of the frost step ( $\mathrm{\SIUnitSymbolCelsius}$ ; log)	2.4	2.25–2.31	2.17–2.38	2.41–2.42
$\theta_{c}$	centre of the connection thresholds	0.4	0.49–0.52	0.54–0.61	0.67–0.70
$s_{\theta}$	width of the connection thresholds (log)	0.15	0.071–0.082	0.048–0.069	0.047–0.058
$T_{v}$	activity threshold of vegetation ( $\mathrm{\SIUnitSymbolCelsius}$ )	8	8.14–8.22	7.67–7.98	8.27–8.37
$s_{v}$	width of the activity threshold ( $\mathrm{\SIUnitSymbolCelsius}$ ; log)	3	4.80–5.18	2.85–3.15	9.33–12.22

Appendix

Table S4: Global constants of CaRT + (learned, one value for all catchments of a dataset; initial value and range of the trained values over three seeds) and fixed constants of both models.

State	Model	Initial state	$n$
snow $N_{k}$	both	0	–
production store / root zone $S$	both	$0.7C$	1460
surface layer $U$	CaRT +	$0.5C_{u}$	1460
near-stream zone $Z$	CaRT +	$0.3C_{z}$	1460
wetness $\Theta=C_{\theta}\theta$	CaRT +	$0.3C_{\theta}$	1460
depressions $V$	CaRT +	$0.5C_{d}$	1460

Appendix

Table S5: Initial states, with spin-up length

n

in days (“–”: no spin-up).

Refinement	Op.	Origin	Nested limit
Connected fraction $A(\theta)$	c, d	exact on the slow manifold; logistic shape, shift and $\theta$ balance postulated	$A_{\min}\to 1$ , outside ( $A_{\min}\leq 0.999$ )
Release exponent	c	asymptotic	$k=0$ , open bound
Viscosity	d	physical	none (no parameter)
Frost	d	heuristic	$a_{F}=0$ , open bound
Near-stream zone	a, b	postulated	$w=0$ , open bound
Surface layer	a	postulated	$\tau_{u}\to 0$ , outside ( $k_{u}\leq 1-e^{-20}$ )

Appendix

Table S6: Summary of the refinements of CaRT + . Op.: operation of Corollary 1 of the main text. Nested limit: in the range (open bound) or outside it (residual effect at the bound in brackets).

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Machine learning models can achieve high predictive accuracy in hydrological applications but often lack physical interpretability. The Mass-Conserving Perceptron (MCP) provides a physics-aware artificial intelligence (AI) framework that enforces conservation principles while allowing hydrological process relationships to be learned from data. In this study, we investigate how progressively embedding physically meaningful representations of hydrological processes within a single MCP storage unit improves predictive skill and interpretability in rainfall-runoff modeling. Starting from a minimal MCP formulation, we sequentially introduce bounded soil storage, state-dependent conductivity, variable porosity, infiltration capacity, surface ponding, vertical drainage, and nonlinear water-table dynamics. The resulting hierarchy of process-aware MCP models is evaluated across 15 catchments spanning five hydroclimatic regions of the continental United States using daily streamflow prediction as the target. Results show that progressively augmenting the internal physical structure of the MCP unit generally improves predictive performance. The influence of these process representations is strongly hydroclimate dependent: vertical drainage substantially improves model skill in arid and snow-dominated basins but reduces performance in rainfall-dominated regions, while surface ponding has comparatively small effects. The best-performing MCP configurations approach the predictive skill of a Long Short-Term Memory benchmark while maintaining explicit physical interpretability. These results demonstrate that embedding hydrological process constraints within AI architectures provides a promising pathway toward interpretable and process-aware rainfall-runoff modeling.

Abstract

Hydrology

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