## 1. Introduction

[2] Long-term mean annual water balance at the watershed scale has been a fundamental research question in hydrological science:

where *P*, *E*, and *Q* are mean annual precipitation, evaporation, and runoff, respectively; Δ*S* is the mean annual change of water storage. *Budyko* [1958] postulated that the partitioning of *P*, to first order, was determined by the competition between available water (*P*) and available energy measured by potential evaporation (*E _{p}*). On the basis of data sets from a large number of watersheds and the work of

*Schreiber*[1904] and

*Ol'dekop*[1911],

*Budyko*[1974] developed a relationship between evaporation ratio (

*E*/

*P*) and climate dryness index (

*E*/

_{p}*P*). In the literature, other functional forms of Budyko-type curves have been developed for the long-term water balance [e.g.,

*Pike*, 1964;

*Fu*, 1981;

*Choudhury*, 1999;

*Zhang et al.*, 2001;

*Porporato et al.*, 2004;

*Yang et al.*, 2008;

*Gerrits et al.*, 2009].

[3] Besides the climate dryness index, the effects of other variables on the mean annual water balance have been studied to explain the observed deviation from the Budyko curve, e.g., the competing effects of climate fluctuations and watershed storage capacity [*Milly*, 1994a, 1994b], rainfall seasonality and soil moisture capacity [*Sankarasubramanian and Vogel*, 2002; *Potter et al.*, 2005; *Hickel and Zhang*, 2006; *Zhang et al.*, 2008], the relative infiltration capacity, relative soil water storage, and the watershed average slope [*Yang et al.*, 2007], climate seasonality, soil properties and topography [*Yokoo et al.*, 2008], vegetation type [*Zhang et al.*, 2001; *Oudin et al.*, 2008], vegetation dynamics [*Donohue et al.*, 2007, 2010], and human activities [*Wang and Hejazi*, 2011].

[4] Recently, water balance estimates at finer temporal scales have been studied, especially the interannual variability of precipitation partitioning. The Budyko-type functions have been extended to study the relationship between the annual evaporation ratio and annual climate dryness index [*Yang et al.*, 2007, 2009; *Zhang et al.*, 2008]. *Potter and Zhang* [2009] tested the relationship with six functional forms of Budyko-type curves and one linear model, and found that rainfall seasonality was important in determining the functional forms. *Jothityangkoon and Sivapalan* [2009] examined the effects of intra-annual variability of rainfall (e.g., storminess and seasonality) on the interannual variability of the annual water balance through the simulation of annual runoff in three semiarid watersheds in Australia and New Zealand.

[5] Similar to equation (1), the water balance at the annual scale is

where *P _{i}*,

*E*, and

_{i}*Q*are annual precipitation, evaporation, and runoff at year

_{i}*i*, respectively; Δ

*S*is the annual water storage change at the watershed scale. The effects of water storage change on annual water balance have been considered in several studies.

_{i}*Pike*'s [1964] functional form was based on the interannual variability of water balance for four watersheds in Malawi. The annual changes in groundwater storage were accounted for by constructing depletion curves under which the area was integrated to obtain a relationship between flow and storage left in the watershed at the end of the dry season. The annual storage change is negligible compared with precipitation and runoff in the four watersheds (Table 1 in the work of

*Pike*[1964]).

*Zhang et al.*[2008] found that Fu's equation, one functional form of Budyko-type curves, performed poorly on estimating annual streamflow in some watersheds in Australia, and they explained that it might be because of the impact of watershed water storage, which could not be neglected at the annual scale.

*Donohue et al.*[2010] studied the annual water balance at 221 watersheds in Australia and found that the effect of nonsteady state conditions was an important source of variation at the annual scale and needed to be accounted for. During multiyear droughts, the annual storage change in the Murray Darling Basin can be up to twice the annual streamflow [

*Leblanc et al.*, 2009].

*Flerchinger*and

*Cooley*[2000] studied the water balance of the Upper Sheep Creek watershed, a 26-ha semiarid mountainous sub-basin within the Reynolds Creek experimental watershed in southwest Idaho, United States. During 1985–1994, the minimum and maximum ratios of annual storage change (including soil moisture and groundwater) to annual precipitation were −0.45 and 0.2, respectively, with the average absolute value of the ratios over the 10 yr being 0.16. The average ratio of annual runoff to annual precipitation (i.e., runoff coefficient) was found to be 0.05. Thus, the annual storage carryover is significant in this watershed.

*Milly and Dunne*[2002] accounted for the interannual storage change in the analysis of discharge variations for 175 large basins worldwide with a median area of 51,000 km

^{2}, and found that the annual storage change effect was important in some basins.

*Wang et al.*[2009] found that the base flow-dominated basins in Nebraska Sand Hills exhibited a negative relationship between and when ignoring Δ

*S*, and that the interannual water storage change was not negligible because of the slow response of the base flow to the interannual change in precipitation.

_{i}Index | USGS Gauge ID | Drainage Area (km^{2}) | P (mm) | E (mm)_{p} | Q (mm) | E_{p}/P | E/P | Q_{s}/Q | Observations | |
---|---|---|---|---|---|---|---|---|---|---|

Soil Moisture | Ground Water | |||||||||

- a
Mean annual precipitation ( *P*), potential evaporation (*E*), streamflow (_{p}*Q*), climate dryness index (*E*), mean annual evaporation ratio (_{p}/P*E/P*) where*E*=*P*−*Q*, the ratio of base flow to the total streamflow (*Q*), and the number of soil moisture and groundwater stations located in each watershed._{s}/Q
| ||||||||||

1 | 3345500 | 3926 | 1025 | 937 | 320 | 0.91 | 0.69 | 0.59 | 2 | 1 |

2 | 3381500 | 8034 | 1091 | 1008 | 373 | 0.92 | 0.66 | 0.50 | 2 | 1 |

3 | 5435500 | 3434 | 887 | 962 | 294 | 1.08 | 0.67 | 0.80 | 1 | 0 |

4 | 5440000 | 2846 | 900 | 916 | 295 | 1.02 | 0.67 | 0.70 | 1 | 0 |

5 | 5447500 | 2598 | 914 | 980 | 270 | 1.07 | 0.70 | 0.73 | 0 | 1 |

6 | 5552500 | 6843 | 899 | 904 | 300 | 1.01 | 0.67 | 0.77 | 0 | 2 |

7 | 5570000 | 4237 | 928 | 1009 | 281 | 1.09 | 0.70 | 0.63 | 1 | 0 |

8 | 5584500 | 1696 | 966 | 995 | 268 | 1.03 | 0.72 | 0.49 | 0 | 1 |

9 | 5585000 | 3349 | 965 | 992 | 267 | 1.03 | 0.72 | 0.51 | 0 | 0 |

10 | 5592500 | 5025 | 1003 | 968 | 311 | 0.97 | 0.69 | 0.68 | 0 | 1 |

11 | 5593000 | 7042 | 1007 | 991 | 290 | 0.98 | 0.71 | 0.73 | 1 | 1 |

12 | 5594000 | 1904 | 1015 | 1018 | 289 | 1.00 | 0.72 | 0.46 | 0 | 0 |

[6] Therefore, the carryover of water storage, through interactions with seasonally varying climate inputs, will have an impact on the amount of runoff produced within the year, and hence mean annual water balance and the inter- and intra-annual variability of runoff yield and water balance [*Zhang et al.*, 2008; *Jothityangkoon and Sivapalan*, 2009; *Cheng et al.*, 2011]. The Budyko framework assumes the steady state of water balance at long-term averages, i.e., in equation (1) [*Donohue et al.*, 2007]; but at the annual scale, the effect of water storage change on the water balance generally needs to be taken into account [*Zhang et al.*, 2008; *Donohue et al.*, 2010]. However, because of the limitation of data availability on *E _{i}* and Δ

*S*, the annual evaporation is usually computed on the basis of by assuming the steady state condition, i.e., [e.g.,

_{i}*Potter and Zhang*, 2009;

*Yang et al.*, 2009].

*It is necessary to examine the extent of which storage carryover affects the annual water balance using storage measurement data directly.*To address this issue, this paper studies the interannual water storage change based on long-term soil moisture and groundwater level measurements in Illinois, and quantifies the impacts of storage change on the water balance at the mean annual and interannual scales. In section 2, the study watersheds and the corresponding data sets are introduced, and then the methods for estimating the storage change at the annual scale are described. The results and discussions are presented in sections 3 and 4, respectively. Conclusions are summarized in the section 5.