ALBERT

Description: General experience in hydrologic modelling suggests that the parameterisation of a model changes over different time and space scales. As a result, hydrologists often re-parameterise their models whenever different temporal or spatial resolutions are required. Here, we investigate theoretical aspects of this issue in a search for the cause(s) of the need for re-parameterisations. Based on Taylor series expansion, we present a mathematical approach for temporal up-scaling that involves covariance-based corrections. We apply the theory using a unique database of half-hourly pan evaporation measurements (comprising 237 days) and examine how the model parameters change when integrating from half-hour to daily and then monthly integration periods. We show that the model parameters change over different integration periods because of changes in the covariance between the model variables. In our model system, we find that the covariance-based correction is highly variable from day to day but settles down to a reasonably constant value over periods longer than about 15 days. The 15 days timescale is likely to be specific to our model system, nonetheless the underlying principle that there is a characteristic timescale for the covariance-based scaling correction of a particular hydrologic process might be general. If that proved true it would open up the possibility of systematically searching for characteristic integration periods for the key covariance-based scaling terms in other key hydrologic processes. That would in turn enable the development of more generalised hydrologic closure scheme(s).

Description: Climate models project increases in globally averaged atmospheric specific humidity that are close to the Clausius–Clapeyron (CC) value of around 7% K−1 whilst projections for mean annual global precipitation (P) and evaporation (E) are somewhat muted at around 2% K−1. Such global projections are useful summaries but do not provide guidance at local (grid box) scales where impacts occur. To bridge that gap in spatial scale, previous research has shown that the "wet get wetter and dry get drier" relation, Δ(P − E) ∝ P − E, follows CC scaling when the projected changes are averaged over latitudinal zones. Much of the research on projected climate impacts has been based on an implicit assumption that this CC relation also holds at local (grid box) scales but this has not previously been examined. In this paper we find that the simple latitudinal average CC scaling relation does not hold at local (grid box) scales over either ocean or land. This means that in terms of P − E, the climate models do not project that the "wet get wetter and dry get drier" at the local scales that are relevant for agricultural, ecological and hydrologic impacts. In an attempt to develop a simple framework for local-scale analysis we found that the climate model output shows a remarkably close relation to the long-standing Budyko framework of catchment hydrology. We subsequently use the Budyko curve and find that the local-scale changes in P − E projected by climate models are dominated by changes in P while the changes in net irradiance at the surface due to greenhouse forcing are small and only play a minor role in changing the mean annual P − E in the climate model projections. To further understand the apparently small changes in net irradiance we also examine projections of key surface energy balance terms. In terms of global averages, we find that the climate model projections are dominated by changes in only three terms of the surface energy balance: (1) an increase in the incoming long-wave irradiance, and the respective responses (2) in outgoing long-wave irradiance and (3) in the evaporative flux, with the latter change being much smaller than the former two terms and mostly restricted to the oceans. The small fraction of the realised surface forcing that is partitioned into E explains why the hydrologic sensitivity (2% K−1) is so much smaller than CC scaling (7% K−1). Much public and scientific perception about changes in the water cycle has been based on the notion that temperature enhances E. That notion is partly true but has proved an unfortunate starting point because it has led to misleading conclusions about the impacts of climate change on the water cycle. A better general understanding of the potential impacts of climate change on water availability that are projected by climate models will surely be gained by starting with the notion that the greater the enhancement of E, the less the surface temperature increase (and vice versa). That latter notion is based on the conservation of energy and is an underlying basis of climate model projections.

Description: General experience in hydrologic modelling suggests that the parameterisation of a model could change over different time scales. As a result, hydrologists often re-parameterise their models whenever different temporal resolutions are required. Here, we investigate theoretical aspects of this issue in a search for the cause(s) of the need for re-parameterisations. Based on Taylor series expansion, we present a mathematical framework for temporal upscaling and evaluate it using a simple experimental system. For that, we use a unique database of half-hourly pan evaporation measurements (comprising 237 days) and examine how the model parameters change for daily and monthly integration periods. We show that the model parameters change over different integration periods with changes in the covariance between the model variables. The theory presented here is general and can be used as a basis for temporal upscaling.

Description: Climate models project increases in globally averaged atmospheric specific humidity at the Clausius–Clapeyron (CC) value of around 7% K−1 whilst projections for precipitation (P) and evaporation (E) are somewhat muted at around 2% K−1. Such global projections are useful summaries but do not provide guidance at local (grid box) scales where impacts occur. To bridge that gap in spatial scale, previous research has shown that the following relation, Δ(P − E) ∝ P − E, holds for zonal averages in climate model projections. In this paper we first test whether that relation holds at grid box scales over ocean and over land. We find that the zonally averaged relation does not hold at grid box scales. We further find that the zonally averaged relation does not hold over land – it is specific to zonal averages over the ocean. As an alternative we tested whether the long-standing Budyko framework of catchment hydrology could be used to synthesise climate model projections over land. We find that climate model projections of Δ(P − E) out to the year 2100 conform closely to the Budyko framework. The analysis also revealed that climate models project little change in the net irradiance at the surface. To understand that result we examined projections of the key surface energy balance terms. In terms of global averages, we find the climate model projections are dominated by changes in only three terms of the surface energy balance; an increase in the incoming longwave irradiance while the responses are (mostly) restricted to the outgoing longwave irradiance with a small change in the evaporative flux. Because the change in outgoing longwave irradiance is a function of the change in surface temperature, we show that the precipitation sensitivity (i.e. 2% K−1) is an accurate summary of the partitioning of the greenhouse-induced surface forcing. With that we demonstrate that the precipitation sensitivity (2% K−1) is less than the CC value (7% K−1) because most of the greenhouse-induced surface forcing is partitioned into outgoing longwave irradiance (instead of evaporation). In essence, the models respond to elevated [CO2] by an increase in atmospheric water vapour content that increases the incoming long-wave irradiance at the surface. The surface response is dominated by a near equal increase in outgoing long-wave irradiance with only minor changes in other terms of the surface energy balance.