Budyko Curve Research Articles

An analytical model for soil-atmosphere feedback

Abstract. Soil-atmosphere feedback is a key for understanding the hydrological cycle and the direction of potential system changes. This paper presents an analytical framework to study the interplay between soil and atmospheric moisture, using as input only the boundary conditions at the upstream end of trajectory, assuming advective moisture transport with average wind speed along this trajectory and vertical moisture exchange with the soil compartment of uniform vertical properties. Precipitation, evaporation from interception and runoff are assumed to depend through simple functional relationships on the soil moisture or the atmospheric moisture. Evaporation from soil moisture (including transpiration) depends on both state variables, which introduces a nonlinear relationship between the two compartments. This nonlinear relationship can explain some apparently paradoxical phenomena such as a local decrease of precipitation accompanied by a runoff increase. The solutions of the resulting water balance equations correspond to two different spatial moisture regimes showing either an increasing or a decreasing atmospheric moisture content along a trajectory starting at the coast, depending on boundary conditions and parameters. The paper discusses how different model parameters (e.g. time scales of precipitation, evaporation or runoff) influence these regimes and how they can create regime switches. Such an analysis has potential to anticipate the range of possible land use and climate changes or to interpret the results of complex land-atmosphere interaction models. Based on derived analytical expressions for the Horton index, the Budyko curve and a precipitation recycling ratio, the analytical framework opens new perspectives for the classification of hydrological systems.

On the effects of seasonality on soil water balance and plant growth

The partitioning of rainfall into evapotranspiration, runoff, and deep infiltration in seasonally dry climates is influenced by strong temporal variability in rainfall and potential evapotranspiration at the intra‐annual scale, which cannot be captured by conventional steady state water balance models. Guided by dimensional analysis and using simplified stochastic soil moisture models, we develop analytical expressions describing the annual partitioning of rainfall into evapotranspiration and deep percolation/runoff in seasonally dry, surface water dependent landscapes. We discuss the related changes to Budyko's curve under different seasonality scenarios, showing that an increase in seasonal rainfall and potential evapotranspiration variability as well as dry season length can lead to a decrease in the annual evapotranspiration ratio. In addition, our model shows that although increased soil water storage can compensate for the decrease in evapotranspiration due to climate seasonality, this effect is more marked in drier climates (higher annual dryness index) compared to wetter climates. Finally, the coupling of the soil moisture model to a minimalist plant growth model shows that in seasonally dry climates, a maximum in biomass is to be expected for a wet season of optimal length, for which the limitations imposed by both water availability and growth duration are at a minimum.

Assessing interannual variability of evapotranspiration at the catchment scale using satellite‐based evapotranspiration data sets

The catchment water‐energy balance at the interannual scale remains a challenge for bridging the important gap in our knowledge of the hydrologic cycle. This study investigates interannual evapotranspiration (ET) variability and water‐energy balance at over 547 catchments across the contiguous United States in different climate zones. The investigation is based on ET data estimated from satellite images and surface daily meteorological data during the period of 1983–2006 provided by the University of Montana. We find that the interannual relationship between annual potential ET to annual precipitation (PET/P) and ET/P, the energy, and water factors defined with the Budyko curve framework can be captured by a linear function, with an average goodness of fit of 0.928 over all the catchments. The linear relationship is validated by another independent remote sensing ET product generated by the University of Washington and is demonstrated to be rational using regression diagnostics. Additionally, a comparison study using a water balance method and the Budyko curve is undertaken to examine the linear relationship. In addition to water supply and energy supply, the primary controls on evapotranspiration, soil water storage, response of vegetation to climate variability, and human interference are also major factors of the interannual relationship between PET/P and ET/P.

The land surface water and energy budgets over the Tibetan Plateau

AbstractTibetan Plateau plays an important role in the Asian Monsoon and global general circulation system. Due to the lack of quantitative observations and complicated cold season processes in high elevation terrain, however, the land surface water and energy budgets are still unexplored over this special region. In this study, the water and energy balances are analyzed in detail based on recently released land surface “reanalysis” data produced by NASA Global Land Data Assimilation System by three different land models, which first ingest all available ground and satellite data into the data assimilation system over the Tibetan Plateau. The major land surface energy and water components in the annual variability are compared. The model and data assimilation skills and deficiencies are also discussed. The total heat fluxes in the transition from heat source to heat sink is observed at the west edge of the TP during winter. But, the area and intensity is far less than the previous hypothesized. The Budyko curve for hydrology indicates that the TP is a typical dry and arid climate where evaporation is mainly controlled by precipitation.

On the role of groundwater and soil texture in the regional water balance: An investigation of the Nebraska Sand Hills, USA

Partitioning of precipitation between evapotranspiration and runoff at the basin scale is primarily controlled by climate and basin characteristics. Here we use the Budyko hypothesis to investigate the impacts of soil texture and groundwater (e.g., baseflow) on annual and long‐term mean annual water balances of basins in a semiarid region located in and around the Sand Hills region of Nebraska, USA. Native grasslands are dominant across the study area with soil textures dramatically different for the Nebraska Sand Hills (primarily sand deposits) and the adjacent regions (mainly less permeable silt loam). For each basin, long‐term hydrologic and meteorological data are obtained, and a baseflow index is calculated using daily streamflow data to quantify the groundwater contribution to streamflow. We found sound field evidence that suggests the control of soil texture on mean annual water balance and the impact of groundwater storage on interannual variability of water balance at catchment scales, which is usually seen at plot scales and in theoretical models. Our results show that compared to the basins located in the adjacent regions, the Nebraska Sand Hills basins experience much higher long‐term mean annual surface runoff ratios (/) and thus lower ratios of ( − )/, where is the long‐term mean annual precipitation. The high baseflow index and its positive correlation with the ratio of / in the Sand Hills basins illustrate the role of lower (higher) evapotranspiration (recharge) rates. On annual time scales, the baseflow‐dominated basins exhibit a negative relationship between annual (P − R) / P and annual aridity index (i.e., the ratio of annual potential evapotranspiration to annual precipitation), which deviates from the original Budyko hypothesis. Moreover, with decreasing baseflow index, this negative relationship gradually transits into a positive relationship that follows Budyko's curves. Our results suggest that soil textural differences may strongly modify the impact of climate on regional water balance. These findings may have important implications for managing water resources under a fluctuating climate.

Analytical derivation of the Budyko curve based on rainfall characteristics and a simple evaporation model

The Budyko curve is often used to estimate the actual evaporation as a function of the aridity index in a catchment. Different empirical equations exist to describe this relationship; however, these equations have very limited physical background. The model concept presented in this paper is physically based and uses only measurable parameters. It makes use of two types of evaporation: interception and transpiration. It assumes that interception can be modeled as a threshold process on a daily time scale. If multiplied with the rainfall distribution function, integrated, and multiplied with the expected number of rain days per month, the monthly interception is obtained. In a similar way, the monthly interception can be upscaled to annual interception. Analogous to the interception process, transpiration can be modeled as a threshold process at a monthly time scale and can be upscaled by integration and multiplication with the expected number of rain months. The expected rain days per month are modeled in two ways: as a fixed proportion of the monthly rainfall and as a power function based on Markov properties of rainfall. The latter is solved numerically. It appears that on an annual basis the analytical model does not differ much from the numerical solution. Hence, the analytical model is used and applied on 10 locations in different climates. This paper shows that the empirical Budyko curve can be constructed on the basis of measurable parameters representing evaporation threshold values and the expected number of rain days and rain months and, in addition, a monthly moisture carryover amount for semiarid zones.

Does evaporation paradox exist in China?

Abstract. One expected consequence of global warming is the increase in evaporation. However, lots of observations show that the rate of evaporation from open pans of water has been steadily decreasing all over the world in the past 50 years. The contrast between expectation and observation is called "evaporation paradox". Based on data from 317 weather stations in China from 1956 to 2005, the trends of pan evaporation and air temperature were obtained and evaporation paradox was analyzed. The conclusions include: (1) From 1956 to 2005, pan evaporation paradox existed in China as a whole while pan evaporation kept decreasing and air temperature became warmer and warmer, but it does not apply to Northeast and Southeast China; (2) From 1956 to 1985, pan evaporation paradox existed narrowly as a whole with unobvious climate warming trend, but it does not apply to Northeast China; (3) From 1986 to 2005, in the past 20 years, pan evaporation paradox did not exist for the whole period while pan evaporation kept increasing, although it existed in South China. Furthermore, the trend of other weather factors including sunshine duration, windspeed, humidity and vapor pressure deficit, and their relations with pan evaporation are discussed. As a result, it can be concluded that pan evaporation decreasing is caused by the decreasing in radiation and wind speed before 1985 and pan evaporation increasing is caused by the decreasing in vapor pressure deficit due to strong warming after 1986. With the Budyko curve, it can be concluded that the actual evaporation decreased in the former 30 years and increased in the latter 20 year for the whole China.

Impact of vegetation coverage on regional water balance in the nonhumid regions of China

The growth of vegetation is affected by water availability, while vegetation growth also feeds back to influence regional water balance. A better understanding of the relationship between vegetation state and water balance would help explain the complicated interactions between climate change, vegetation dynamics, and the water cycle. In the present study, the impact of vegetation coverage on regional water balance was analyzed under the framework of the Budyko hypothesis by using data from 99 catchments in the nonhumid regions of China, including the Inland River basin, the Hai River basin, and the Yellow River basin. The distribution of vegetation coverage on the Budyko curve was analyzed, and it was found that a wetter environment (higher P/E0) had a higher vegetation coverage (M) and was associated with a higher evapotranspiration efficiency (E/E0). Moreover, vegetation coverage was related not only to climate conditions (measured by the dryness index DI = E0/P) but also to landscape conditions (measured by the parameter n in the coupled water–energy balance equation). This suggests that the regional long‐term water balance should not vary along a single Budyko curve; instead, it should form a group of Budyko curves owing to the interactions between vegetation, climate, and water cycle. A positive correlation was found between water balance component (E/P) and vegetation coverage (M) for most of the Yellow River basin and for the Inland River basin, while a negative correlation of M ∼ E/P was found in the Hai River basin. Vegetation coverage was successfully incorporated into an empirical equation for estimating the catchment landscape parameter n in the coupled water–energy balance equation. It was found that interannual variability in vegetation coverage could improve the estimation of the interannual variability in regional water balance.

On the importance of including vegetation dynamics in Budyko's hydrological model

Abstract. The Budyko curve describes the patterns observed between between climate, evapotranspiration and run-off and has proven to be a useful model for predicting catchment energy and water balances. In this paper we review the Budyko curve's underlying framework and, based on the literature, present an argument for why it is important to include vegetation dynamics into the framework for some purposes. The Budyko framework assumes catchments are at steady-state and are driven by the macro-climate, two conditions dependent on the scales of application, such that the framework's reliability is greatest when applied using long-term averages (≫1 year) and to large catchments (>10 000 km2). At these scales previous experience has shown that the hydrological role of vegetation does not need to be explicitly considered within the framework. By demonstrating how dynamics in the leaf area, photosynthetic capacity and rooting depth of vegetation affect not only annual and seasonal vegetation water use, but also steady-state conditions, we argue that it is necessary to explicitly include vegetation dynamics into the Budyko framework before it is applied at small scales. Such adaptations would extend the framework not only to applications at small timescales and/or small catchments but to operational activities relating to vegetation and water management.

A monthly interception equation based on the statistical characteristics of daily rainfall

This paper presents a simple analytical equation for monthly interception on the basis of the combination of a daily threshold model with the probability distribution of daily rainfall. In this paper, interception has a wider definition than merely canopy interception. It is the part of the rainfall that evaporates after it has been stored on the wetted surface, which includes the canopy, the understory, the bottom vegetation, the litter layer, the soil, and the hard surface. Interception is defined as the process of evaporation from intercepted rainfall. It is shown that this process has a typical timescale of 1 day. Monthly interception models can be improved by taking the statistical characteristics of daily rainfall into account. These characteristics appear to be less variable in space than the rainfall itself. With the statistical characteristics of daily rainfall obtained at a few locations where reliable records are available (for example, airports) monthly models can be improved and applied to larger areas (20–200 km). The equation can be regionalized, making use of the Markov property of daily rainfall. The equation obtained for monthly interception is similar to Budyko's curve.

Correction of Global Precipitation Products for Orographic Effects

AbstractUnderestimation of precipitation in topographically complex regions plagues most gauge-based gridded precipitation datasets. Gauge locations are usually in or near population centers, which tend to lie at low elevations relative to the surrounding terrain. For hydrologic modeling purposes, the resulting bias can result in serious underprediction of observed flows. A hydrologic water balance approach to develop a globally consistent correction for the underestimation of gridded precipitation in mountainous regions is described. The adjustment is based on a combination of the catchment water balances and variations of the Budyko E/P versus/P curve. The method overlays streamflow measurements onto watershed boundaries and then performs watershed water balances to determine “true” precipitation. Rather than relying on a modeled runoff ratio, evaporation is estimated using the Budyko curves. The average correction ratios for each of 357 mountainous river basins worldwide are spatially distributed across the basins and are then interpolated to ungauged areas. Following application of adjustments for precipitation catch deficiencies, the correction ratios are used to scale monthly precipitation from an existing monthly global dataset (1979–99, 0.5° resolution). The correction for orographic effects resulted in a net increase in global terrestrial precipitation of 6.2% (20.2% in orographically influenced regions only) for the 1979–99 climatology. The approach developed here is applicable to any precipitation dataset in regions where good streamflow data exist. As a cautionary note, the correction factors are dataset dependent, and therefore the adjustments are strictly applicable only to the data from which they were derived.