On hydrological model complexity, its geometrical interpretations and prediction uncertainty

Knowledge of hydrological model complexity can aid selection of an optimal prediction model out of a set of available models. Optimal model selection is formalized as selection of the least complex model out of a subset of models that have lower empirical risk. This may be considered equivalent to minimizing an upper bound on prediction error, defined here as the mathematical expectation of empirical risk. In this paper, we derive an upper bound that is free from assumptions on data and underlying process distribution as well as on independence of model predictions over time. We demonstrate that hydrological model complexity, as defined in the presented theoretical framework, plays an important role in determining the upper bound. The model complexity also acts as a stabilizer to a hydrological model selection problem if it is deemed ill-posed. We provide an algorithm for computing complexity of any arbitrary hydrological model. We also demonstrate that hydrological model complexity has a geometric interpretation as the size of model output space. The presented theory is applied to quantify complexities of two hydrological model structures: SAC-SMA and SIXPAR. It detects that SAC-SMA is indeed more complex than SIXPAR. We also develop an algorithm to estimate the upper bound on prediction error, which is applied on five different rainfall-runoff model structures that vary in complexity. We show that a model selection problem is stabilized by regularizing it with model complexity. Complexity regularized model selection yields models that are robust in predicting future but yet unseen data.Water ManagementCivil Engineering and Geoscience

Endogenous change: On cooperation and water availability in two ancient societies

We propose and test the theory of endogenous change in societal institutions based on historical reconstructions of two ancient civilizations, the Indus and Hohokam, in two water-scarce basins, the Indus Basin in the Indian subcontinent and the lower Colorado Basin in the southwestern United States. In our reconstructions, institutions are approximated by the scale of “cooperation”, be it in the form of the extent of trade, sophisticated irrigation networks, a central state or a loosely held state with a common cultural identity. We study changes in institutions brought about by changes in factors like rainfall, population density, and land-use-induced water resource availability, in a proximate manner. These factors either change naturally or are changed by humans; in either case we contend that the changes affect the stability of cooperative structures over time. We relate the quantitative dimensions of water access by ancient populations to the co-evolution of water access and the socioeconomic and sociopolitical organizations. In doing so, we do not claim that water manipulation was the single most significant factor in stimulating social development and complexity – this would be highly reductionist. Nonetheless, we provide a discussion with the aim to enhance our understanding of the complexity of coupled human–hydrological systems. We find that scarcity triggered more complex cooperative arrangements in both Indus and Hohokam societies.Water ManagementCivil Engineering and Geoscience

Hydro-social Metabolism: Scaling of birth rate with regional water use

opulation growth is often intuitively linked with proportionally higher use of fresh water resources. However, this implies that water use per capita does not change with population growth. We not only find that birth rates of regions are negatively related with its water use per capita (i.e., higher birth rate is associated with lower water use), but also that birth rates scale with the latter with a negative power. We use population and water withdrawal data from 1950 to 2005 at irregular 5-year intervals; with virtual water content, virtual water trade and agricultural production data from 1960 to 2000 for the seven continents to investigate the scaling relationship and interpret it through the lens of metabolism theory. Our analysis reveals that the scaling exponent lies between −1/3 and −1/2. Deviations from the power relationship are observed for Europe and Africa, which are attributed to lower than expected and higher than expected birth rates, respectively. Europe’s deviation from the average scaling relationship may be due to the higher rate of return on human capital in industrialized countries. But why Africa deviates, while other developing and developed regions follow the power relationship more closely, remains a puzzle.Water Resource

Hydro-social metabolism: Scaling of birth rates with regional water use

Water Resource

Endogenous change: On cooperation and water in ancient history

We propose and test the theory of endogenous change based on historical reconstructions of two ancient civilizations, Indus and Hohokam, in two water scarce basins, the Indus basin in the Indian subcontinent and the Lower Colorado basin in Southwestern United States. The endogenous institutional change sees changes in institutions as a sequence of equilibria brought about by changes in “quasi-parameters” such as rainfall, population density, soil and land use induced water resource availability. In the historical reconstructions of ancient civilizations, institutions are proximated by the scale of cooperation be it in the form of the extent of trade, sophisticated irrigation network, a centrally planned state or a loosely held state with a common cultural identity. The “quasi-parameters” either change naturally or are changed by humans and the changes affect the stability of cooperative structures over time. However, human influenced changes in the quasi-parameters itself are conditioned on the scale of existing cooperative structures. We thus provide insights into the quantitative dimensions of water access by ancient populations and its co-evolution with the socioeconomic and sociopolitical organization of the human past. We however do not suggest that water manipulation was the single most significant factor in stimulating social development and complexity – clearly this has been shown as highly reductionist, even misleading. The paper cautiously contributes to proximate prediction of hydrological change by attempting to understand the complexity of coupled human-hydrological systems.Water ManagementCivil Engineering and Geoscience

Decent wage is more important than absolution of debts: A smallholder socio-hydrological modelling framework

Water ManagementCivil Engineering and Geoscience

Interlinkages between human agency, water use efficiency and sustainable food production

Efficient use of water and nutrients in crop production are critical for sustainable water and crop production systems. Understanding the role of humans in ensuring water and nutrient use efficiency is therefore an important ingredient of sustainable development. Crop production functions are often defined either as functions of water and nutrient deficiency or are based on economic production theory that conceptualizes production as a result of economic activities that take in inputs such as water, capital and labor and produce crop biomass as output. This paper fills a gap by consistently treating water and nutrient use and human agency in crop production, thus providing a better understanding of the role humans play in crop production. Uptake of water and nutrients are two dominant biophysical processes of crop growth while human agency, including irrigation machine power, land-preparing machine power and human labor force, determine limits of water and nutrient resources that are accessible to crops. Two crops, i.e., winter wheat and rice, which account for the majority of food crop production are considered in a rapidly developing region of the world, Jiangsu Province, China, that is witnessing the phenomenon of rural to urban migration. Its production is modeled in two steps. First water and nutrient efficiencies, defined as the ratios of observed uptake to quantities applied, are modeled as functions of labor and machine power (representing human agency). In the second step, crop yields are modeled as functions of water and nutrient efficiencies multiplied by amounts of water and fertilizers applied. As a result, crop production is predicted by first simulating water and nutrient uptake efficiencies and then determining yield as a function of water and nutrients that are actually taken up by crops. Results show that modeled relationship between water use efficiency and human agency explains 68% of observed variance for wheat and 49% for rice. The modeled relationship between nutrient use efficiency and human agency explains 49% of the variance for wheat and 56% for rice. The modeled relationships between yields and actual uptakes in the second step explain even higher percentages of observed the variance: 73% for wheat and 84% for rice. Leave-one-out cross validation of yield predictions shows that relative errors are on average within 5% of the observed yields, reinforcing the robustness of the estimated relationship and of conceptualizing crop production as a composite function of bio-physical mechanism and human agency. Interpretations based on the model reveal that after 2005, mechanization gradually led to less labor being used relative to machinery to achieve same levels of water use efficiency. Labor and irrigation equipment, on the other hand, were found to be complimentary inputs to water use efficiency. While the results suggest interventions targeting machinery are most instrumental in increasing wheat productivity, they may exasperate rural – urban migration. Policy strategies for alleviating rural-urban migration while ensuring regional food security can nonetheless be devised where appropriate data are available.Accepted Author ManuscriptWater Resource

Endogeneity in water use behaviour across case studies of household water treatment adoption in developing countries

Endogeneity or reverse causality in regression analysis results in biased estimation of the effects of independent variables on the dependent variable and leads to inaccurate interpretations. However, the biased estimation of the effects of psychological factors on water–related behaviours are rarely discussed. This study investigated the endogeneity of psychological factors in water-related behaviour using an instrument variable (IV) approach. Data from eight household water treatment (HWT) studies in Asia, Africa, and South America were utilized. A combination of several socio-economic characteristics, such as education and accessibility, was used as a control variable and three psychological factors, i.e., perception of risk, attitude towards HWT, and social norms, were used as the predictors of the adoption of HWT. Variables related to institutional quality of the countries, based on the World Governance Indicators of the World Bank were used as IVs to predict the psychological factors. The results suggest that endogeneity exists in water-related behavioural studies. Institutions were found to be valid IV for psychological factors attitude and norms, but not for the perception of risk. This suggests that the institutional quality influences households’ attitude and norms regarding behaviour. If the feedback effect of actual behaviour on the psychological factors were not considered, the effects of attitude and norms on HWT adoption were underestimated by 59% and 40%, respectively. Finally, despite the challenge of finding valid IV, the endogeneity effect of psychological factors needs to be controlled when estimating the effect of psychological factors on water-related behaviour in future water-related behavioural studies.Sanitary EngineeringWater ResourcesWater Managemen

A comparative study of the influence of socio-environmental characteristics on psychosocial factors that trigger adoption of household water treatment in developing countries

Household water treatment (HWT) is a simple technology to tackle this issue of non-potable drinking water at household level. Unfortunately, studies have showed that people do not use it regularly which diminishes the impact of HWT on health.Sanitary EngineeringWater Resource

Socio-Economic and Psychological Determinants for Household Water Treatment Practices in Indigenous–Rural Indonesia

Household water treatment (HWT) is one of the possible technologies to improve the quality of potable water in low–middle-income countries. However, many households still drink untreated water that leads to negative health consequences, highlighting the need for a behavioral study. This study explores the role of eight socio-economic characteristics (SECs) and five psychological factors on the practices of HWT, using a combination of statistical analyses and Bayesian Belief Network (BBN) modeling. The findings were based on 377 household interviews in East Sumba, Indonesia, an area where indigenous belief is still common. Self-reported answers and observed practices of HWT were combined, and 51% of the respondents were categorized as regular users of HWT. Furthermore, favorable socio-economic conditions, e.g., wealthier or more educated parents, facilitated psychological factors that led to regular use of HWT. This suggests the importance of reducing SEC inequalities to improve the HWT adoption. Mother's education was the most influential SEC (ΔP = 8), and people who followed indigenous beliefs tend not to use HWT on a regular basis. Moreover, easy access to water positively influenced the household's ability to operate the HWT technology. Attitude toward the HWT practice, especially the perception of treated water's taste (β = 0.277), was the most significant psychological factor, influencing HWT adoption. An interpretation of complex interlinkages between socio-economic conditions and psychological factors that drive the practice of HWT was therefore offered, alongside recommendations for conservative interventions to change the household's behavior in a culturally unique area with difficult access to water.Sanitary EngineeringWater ResourcesWater Managemen